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Conditions for Regression Inference: Legacy Diagnostic Guide

36 visible MCQs, 14 FRQ sets, formulas, worked answers, and direct links to the complete AP Statistics practice system.

Published July 18, 2026Updated August 7, 2026By Engr. Muhammad Yar Saqib44 min read
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AP Statistics Practice

Conditions for Regression Inference: Legacy Diagnostic Guide

Conditions for Regression Inference: Legacy Diagnostic Guide practice bank: Solve the visible multiple-choice and free-response questions, then compare every step with the worked answers.

MCQs36
FRQ sets14
AnswersVisible
Topic links73 pages

Conditions for Regression Inference: Legacy Diagnostic Guide: formulas and targets

t statistict=(b−β0)SEb
dfn−2

Inference for a Regression Slope (Legacy/Enrichment) multiple-choice practice

Question 1. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a housing authority in Midwest consortium during a monthly quality review has slope b=1.52, SEb=0.464, and n=47. Test H0:β=0, and identify the revised-2027 status.

  1. A. Use df=n−1 because every regression has one parameter.
  2. B. Test H0:r=1 because correlation and slope are identical.
  3. C. The test is current Unit 5 required inference for 2027.
  4. D. t=3.276, df=45, p=0.002; legacy/enrichment for 2027.

Answer: D

t=b/SEb=1.520.464=3.276, df=45, two-sided p=0.002. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=3.276, df=45, p=0.002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=3.276, df=45, p=0.002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=3.276, df=45, p=0.002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 2. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a county library in Pine Ridge during a two-month observation window has slope b=1.302, SEb=0.198, and n=46. Test H0:β=0, and identify the revised-2027 status.

  1. A. Use df=n−1 because every regression has one parameter.
  2. B. t=6.576, df=44, p=0; legacy/enrichment for 2027.
  3. C. The test is current Unit 5 required inference for 2027.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: B

t=b/SEb=1.3020.198=6.576, df=44, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=6.576, df=44, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=6.576, df=44, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=6.576, df=44, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 3. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a solar installer in Metro East during a multiweek validation study has slope b=1.612, SEb=0.473, and n=26. Test H0:β=0, and identify the revised-2027 status.

  1. A. Use df=n−1 because every regression has one parameter.
  2. B. Test H0:r=1 because correlation and slope are identical.
  3. C. The test is current Unit 5 required inference for 2027.
  4. D. t=3.408, df=24, p=0.0023; legacy/enrichment for 2027.

Answer: D

t=b/SEb=1.6120.473=3.408, df=24, two-sided p=0.0023. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=3.408, df=24, p=0.0023; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=3.408, df=24, p=0.0023; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=3.408, df=24, p=0.0023; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 4. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a regional hospital in Capital Region during a summer implementation review has slope b=0.311, SEb=0.476, and n=37. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. t=0.653, df=35, p=0.5178; legacy/enrichment for 2027.
  3. C. Test H0:r=1 because correlation and slope are identical.
  4. D. Use df=n−1 because every regression has one parameter.

Answer: B

t=b/SEb=0.3110.476=0.653, df=35, two-sided p=0.5178. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=0.653, df=35, p=0.5178; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=0.653, df=35, p=0.5178; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=0.653, df=35, p=0.5178; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 5. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a state park in Prairie District during a six-week field trial has slope b=1.116, SEb=0.501, and n=51. Test H0:β=0, and identify the revised-2027 status.

  1. A. t=2.228, df=49, p=0.0305; legacy/enrichment for 2027.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. Test H0:r=1 because correlation and slope are identical.
  4. D. Use df=n−1 because every regression has one parameter.

Answer: A

t=b/SEb=1.1160.501=2.228, df=49, two-sided p=0.0305. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=2.228, df=49, p=0.0305; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=2.228, df=49, p=0.0305; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=2.228, df=49, p=0.0305; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 6. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a recycling program in Pacific Northwest during a spring 2027 pilot has slope b=0.421, SEb=0.349, and n=23. Test H0:β=0, and identify the revised-2027 status.

  1. A. t=1.206, df=21, p=0.2411; legacy/enrichment for 2027.
  2. B. Use df=n−1 because every regression has one parameter.
  3. C. The test is current Unit 5 required inference for 2027.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: A

t=b/SEb=0.4210.349=1.206, df=21, two-sided p=0.2411. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=1.206, df=21, p=0.2411; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=1.206, df=21, p=0.2411; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=1.206, df=21, p=0.2411; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 7. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a digital learning platform in Coastal Plains during a quarterly performance study has slope b=0.949, SEb=0.263, and n=22. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. t=3.608, df=20, p=0.0018; legacy/enrichment for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: B

t=b/SEb=0.9490.263=3.608, df=20, two-sided p=0.0018. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=3.608, df=20, p=0.0018; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=3.608, df=20, p=0.0018; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=3.608, df=20, p=0.0018; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 8. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a solar installer in Lakeside district during a fall 2026 audit has slope b=0.699, SEb=0.171, and n=48. Test H0:β=0, and identify the revised-2027 status.

  1. A. Use df=n−1 because every regression has one parameter.
  2. B. Test H0:r=1 because correlation and slope are identical.
  3. C. t=4.088, df=46, p=0.0002; legacy/enrichment for 2027.
  4. D. The test is current Unit 5 required inference for 2027.

Answer: C

t=b/SEb=0.6990.171=4.088, df=46, two-sided p=0.0002. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=4.088, df=46, p=0.0002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=4.088, df=46, p=0.0002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=4.088, df=46, p=0.0002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 9. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a community bank in Riverbend during a weekday operations study has slope b=0.821, SEb=0.311, and n=26. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. Use df=n−1 because every regression has one parameter.
  3. C. The test is current Unit 5 required inference for 2027.
  4. D. t=2.64, df=24, p=0.0143; legacy/enrichment for 2027.

Answer: D

t=b/SEb=0.8210.311=2.64, df=24, two-sided p=0.0143. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=2.64, df=24, p=0.0143; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=2.64, df=24, p=0.0143; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=2.64, df=24, p=0.0143; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 10. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a regional airport authority in Central County during a quarterly performance study has slope b=1, SEb=0.188, and n=36. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. t=5.319, df=34, p=0; legacy/enrichment for 2027.
  4. D. Use df=n−1 because every regression has one parameter.

Answer: C

t=b/SEb=10.188=5.319, df=34, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=5.319, df=34, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=5.319, df=34, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=5.319, df=34, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 11. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a farm cooperative in South Harbor during a baseline measurement week has slope b=0.74, SEb=0.173, and n=22. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. t=4.277, df=20, p=0.0004; legacy/enrichment for 2027.

Answer: D

t=b/SEb=0.740.173=4.277, df=20, two-sided p=0.0004. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=4.277, df=20, p=0.0004; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=4.277, df=20, p=0.0004; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=4.277, df=20, p=0.0004; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 12. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a state park in Pine Ridge during a semester-long cohort study has slope b=1.58, SEb=0.543, and n=51. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. t=2.91, df=49, p=0.0054; legacy/enrichment for 2027.

Answer: D

t=b/SEb=1.580.543=2.91, df=49, two-sided p=0.0054. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=2.91, df=49, p=0.0054; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=2.91, df=49, p=0.0054; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=2.91, df=49, p=0.0054; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 13. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a community college in Midwest consortium during a six-week field trial has slope b=0.368, SEb=0.22, and n=34. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. t=1.673, df=32, p=0.1041; legacy/enrichment for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. The test is current Unit 5 required inference for 2027.

Answer: B

t=b/SEb=0.3680.22=1.673, df=32, two-sided p=0.1041. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=1.673, df=32, p=0.1041; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=1.673, df=32, p=0.1041; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=1.673, df=32, p=0.1041; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 14. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a university advising center in Metro East during a school-year data collection has slope b=0.474, SEb=0.209, and n=51. Test H0:β=0, and identify the revised-2027 status.

  1. A. Use df=n−1 because every regression has one parameter.
  2. B. Test H0:r=1 because correlation and slope are identical.
  3. C. t=2.268, df=49, p=0.0278; legacy/enrichment for 2027.
  4. D. The test is current Unit 5 required inference for 2027.

Answer: C

t=b/SEb=0.4740.209=2.268, df=49, two-sided p=0.0278. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=2.268, df=49, p=0.0278; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=2.268, df=49, p=0.0278; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=2.268, df=49, p=0.0278; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 15. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a city transit agency in Capital Region during a summer implementation review has slope b=1.317, SEb=0.201, and n=55. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. Test H0:r=1 because correlation and slope are identical.
  3. C. t=6.552, df=53, p=0; legacy/enrichment for 2027.
  4. D. Use df=n−1 because every regression has one parameter.

Answer: C

t=b/SEb=1.3170.201=6.552, df=53, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=6.552, df=53, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=6.552, df=53, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=6.552, df=53, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 16. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a county election office in Central County during a follow-up evaluation period has slope b=1.094, SEb=0.501, and n=30. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. t=2.184, df=28, p=0.0375; legacy/enrichment for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. The test is current Unit 5 required inference for 2027.

Answer: B

t=b/SEb=1.0940.501=2.184, df=28, two-sided p=0.0375. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=2.184, df=28, p=0.0375; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=2.184, df=28, p=0.0375; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=2.184, df=28, p=0.0375; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 17. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a recycling program in Pacific Northwest during a baseline measurement week has slope b=1.558, SEb=0.193, and n=22. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. Use df=n−1 because every regression has one parameter.
  3. C. t=8.073, df=20, p=0; legacy/enrichment for 2027.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: C

t=b/SEb=1.5580.193=8.073, df=20, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=8.073, df=20, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=8.073, df=20, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=8.073, df=20, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 18. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a regional manufacturer in Prairie District during a winter readiness review has slope b=0.567, SEb=0.335, and n=44. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. Test H0:r=1 because correlation and slope are identical.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. t=1.693, df=42, p=0.098; legacy/enrichment for 2027.

Answer: D

t=b/SEb=0.5670.335=1.693, df=42, two-sided p=0.098. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=1.693, df=42, p=0.098; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=1.693, df=42, p=0.098; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=1.693, df=42, p=0.098; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 19. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a regional manufacturer in Mountain Region during a follow-up evaluation period has slope b=0.916, SEb=0.388, and n=37. Test H0:β=0, and identify the revised-2027 status.

  1. A. Use df=n−1 because every regression has one parameter.
  2. B. Test H0:r=1 because correlation and slope are identical.
  3. C. The test is current Unit 5 required inference for 2027.
  4. D. t=2.361, df=35, p=0.0239; legacy/enrichment for 2027.

Answer: D

t=b/SEb=0.9160.388=2.361, df=35, two-sided p=0.0239. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=2.361, df=35, p=0.0239; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=2.361, df=35, p=0.0239; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=2.361, df=35, p=0.0239; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 20. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a food safety laboratory in Cedar Grove during a spring 2027 pilot has slope b=1.017, SEb=0.183, and n=41. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. t=5.557, df=39, p=0; legacy/enrichment for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: B

t=b/SEb=1.0170.183=5.557, df=39, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=5.557, df=39, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=5.557, df=39, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=5.557, df=39, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 21. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a housing authority in Central County during a pre-exam training cycle has slope b=0.624, SEb=0.331, and n=53. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. t=1.885, df=51, p=0.0651; legacy/enrichment for 2027.

Answer: D

t=b/SEb=0.6240.331=1.885, df=51, two-sided p=0.0651. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=1.885, df=51, p=0.0651; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=1.885, df=51, p=0.0651; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=1.885, df=51, p=0.0651; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 22. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a university advising center in Cedar Grove during a follow-up evaluation period has slope b=0.743, SEb=0.267, and n=50. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. t=2.783, df=48, p=0.0077; legacy/enrichment for 2027.
  4. D. Use df=n−1 because every regression has one parameter.

Answer: C

t=b/SEb=0.7430.267=2.783, df=48, two-sided p=0.0077. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=2.783, df=48, p=0.0077; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=2.783, df=48, p=0.0077; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=2.783, df=48, p=0.0077; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 23. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a university advising center in Cedar Grove during a school-year data collection has slope b=1.105, SEb=0.271, and n=43. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. t=4.077, df=41, p=0.0002; legacy/enrichment for 2027.

Answer: D

t=b/SEb=1.1050.271=4.077, df=41, two-sided p=0.0002. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=4.077, df=41, p=0.0002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=4.077, df=41, p=0.0002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=4.077, df=41, p=0.0002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 24. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a school district in Prairie District during a winter readiness review has slope b=1.372, SEb=0.335, and n=49. Test H0:β=0, and identify the revised-2027 status.

  1. A. Use df=n−1 because every regression has one parameter.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. Test H0:r=1 because correlation and slope are identical.
  4. D. t=4.096, df=47, p=0.0002; legacy/enrichment for 2027.

Answer: D

t=b/SEb=1.3720.335=4.096, df=47, two-sided p=0.0002. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=4.096, df=47, p=0.0002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=4.096, df=47, p=0.0002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=4.096, df=47, p=0.0002; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 25. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a farm cooperative in Desert County during a weekday operations study has slope b=0.956, SEb=0.4, and n=22. Test H0:β=0, and identify the revised-2027 status.

  1. A. Use df=n−1 because every regression has one parameter.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. t=2.39, df=20, p=0.0268; legacy/enrichment for 2027.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: C

t=b/SEb=0.9560.4=2.39, df=20, two-sided p=0.0268. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=2.39, df=20, p=0.0268; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=2.39, df=20, p=0.0268; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=2.39, df=20, p=0.0268; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 26. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a community bank in Great Lakes during a weekday operations study has slope b=0.493, SEb=0.427, and n=32. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. t=1.155, df=30, p=0.2574; legacy/enrichment for 2027.
  3. C. Test H0:r=1 because correlation and slope are identical.
  4. D. Use df=n−1 because every regression has one parameter.

Answer: B

t=b/SEb=0.4930.427=1.155, df=30, two-sided p=0.2574. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=1.155, df=30, p=0.2574; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=1.155, df=30, p=0.2574; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=1.155, df=30, p=0.2574; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 27. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a municipal emergency dispatch center in Coastal Plains during a fall 2026 audit has slope b=1.9, SEb=0.209, and n=43. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. t=9.091, df=41, p=0; legacy/enrichment for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: B

t=b/SEb=1.90.209=9.091, df=41, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=9.091, df=41, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=9.091, df=41, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=9.091, df=41, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 28. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a county election office in Sunbelt district during a quarterly performance study has slope b=0.319, SEb=0.542, and n=48. Test H0:β=0, and identify the revised-2027 status.

  1. A. t=0.589, df=46, p=0.559; legacy/enrichment for 2027.
  2. B. Use df=n−1 because every regression has one parameter.
  3. C. The test is current Unit 5 required inference for 2027.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: A

t=b/SEb=0.3190.542=0.589, df=46, two-sided p=0.559. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=0.589, df=46, p=0.559; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=0.589, df=46, p=0.559; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=0.589, df=46, p=0.559; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 29. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a county library in Sunbelt district during a baseline measurement week has slope b=1.51, SEb=0.526, and n=29. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. Use df=n−1 because every regression has one parameter.
  3. C. t=2.871, df=27, p=0.0079; legacy/enrichment for 2027.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: C

t=b/SEb=1.510.526=2.871, df=27, two-sided p=0.0079. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=2.871, df=27, p=0.0079; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=2.871, df=27, p=0.0079; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=2.871, df=27, p=0.0079; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 30. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a public high school in Sunbelt district during a summer implementation review has slope b=1.612, SEb=0.407, and n=30. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. Use df=n−1 because every regression has one parameter.
  4. D. t=3.961, df=28, p=0.0005; legacy/enrichment for 2027.

Answer: D

t=b/SEb=1.6120.407=3.961, df=28, two-sided p=0.0005. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=3.961, df=28, p=0.0005; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=3.961, df=28, p=0.0005; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=3.961, df=28, p=0.0005; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 31. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a city recreation department in Lakeside district during a randomized pilot period has slope b=0.392, SEb=0.429, and n=20. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. The test is current Unit 5 required inference for 2027.
  3. C. t=0.914, df=18, p=0.3729; legacy/enrichment for 2027.
  4. D. Use df=n−1 because every regression has one parameter.

Answer: C

t=b/SEb=0.3920.429=0.914, df=18, two-sided p=0.3729. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=0.914, df=18, p=0.3729; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=0.914, df=18, p=0.3729; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=0.914, df=18, p=0.3729; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 32. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a school district in Pine Ridge during a regional benchmarking study has slope b=0.547, SEb=0.347, and n=28. Test H0:β=0, and identify the revised-2027 status.

  1. A. The test is current Unit 5 required inference for 2027.
  2. B. Use df=n−1 because every regression has one parameter.
  3. C. Test H0:r=1 because correlation and slope are identical.
  4. D. t=1.576, df=26, p=0.127; legacy/enrichment for 2027.

Answer: D

t=b/SEb=0.5470.347=1.576, df=26, two-sided p=0.127. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=1.576, df=26, p=0.127; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=1.576, df=26, p=0.127; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=1.576, df=26, p=0.127; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 33. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a recycling program in Sunbelt district during a follow-up evaluation period has slope b=1.592, SEb=0.287, and n=37. Test H0:β=0, and identify the revised-2027 status.

  1. A. t=5.547, df=35, p=0; legacy/enrichment for 2027.
  2. B. Use df=n−1 because every regression has one parameter.
  3. C. The test is current Unit 5 required inference for 2027.
  4. D. Test H0:r=1 because correlation and slope are identical.

Answer: A

t=b/SEb=1.5920.287=5.547, df=35, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=5.547, df=35, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=5.547, df=35, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=5.547, df=35, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 34. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a farm cooperative in Coastal Plains during a winter readiness review has slope b=0.709, SEb=0.348, and n=46. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. Use df=n−1 because every regression has one parameter.
  3. C. t=2.037, df=44, p=0.0477; legacy/enrichment for 2027.
  4. D. The test is current Unit 5 required inference for 2027.

Answer: C

t=b/SEb=0.7090.348=2.037, df=44, two-sided p=0.0477. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=2.037, df=44, p=0.0477; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=2.037, df=44, p=0.0477; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=2.037, df=44, p=0.0477; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 35. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a county library in Atlantic Corridor during a randomized pilot period has slope b=1.886, SEb=0.174, and n=33. Test H0:β=0, and identify the revised-2027 status.

  1. A. Test H0:r=1 because correlation and slope are identical.
  2. B. Use df=n−1 because every regression has one parameter.
  3. C. The test is current Unit 5 required inference for 2027.
  4. D. t=10.839, df=31, p=0; legacy/enrichment for 2027.

Answer: D

t=b/SEb=1.8860.174=10.839, df=31, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=10.839, df=31, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=10.839, df=31, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: t=10.839, df=31, p=0; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Question 36. Inference for a Regression Slope (Legacy/Enrichment)

A regression sample at a county library in Midwest consortium during a winter readiness review has slope b=0.588, SEb=0.544, and n=45. Test H0:β=0, and identify the revised-2027 status.

  1. A. Use df=n−1 because every regression has one parameter.
  2. B. Test H0:r=1 because correlation and slope are identical.
  3. C. t=1.081, df=43, p=0.2858; legacy/enrichment for 2027.
  4. D. The test is current Unit 5 required inference for 2027.

Answer: C

t=b/SEb=0.5880.544=1.081, df=43, two-sided p=0.2858. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: t=1.081, df=43, p=0.2858; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: t=1.081, df=43, p=0.2858; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: t=1.081, df=43, p=0.2858; legacy/enrichment for 2027. Key check: The test evaluates the population slope β, not the sample slope b.

Inference for a Regression Slope (Legacy/Enrichment) free-response practice

10-point analytic study rubric used for the sets below
EvidencePoints
Correct target, notation, direction, or group order2
Correct method/model and defensible conditions2
Correct setup and execution3
Contextual interpretation and scope/limitation2
Clear communication with units and labels1

FRQ set 1: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a community bank in Mountain Region during a two-month observation window has slope b=1.333, SEb=0.434, and n=43. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=1.3330.434=3.071, df=41, two-sided p=0.0038. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 2: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a municipal emergency dispatch center in Great Lakes during a six-week field trial has slope b=0.815, SEb=0.315, and n=53. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=0.8150.315=2.587, df=51, two-sided p=0.0126. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 3: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a county election office in Desert County during a pre-exam training cycle has slope b=0.632, SEb=0.223, and n=21. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=0.6320.223=2.834, df=19, two-sided p=0.0106. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 4: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a regional hospital in Prairie District during a winter readiness review has slope b=0.72, SEb=0.523, and n=52. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=0.720.523=1.377, df=50, two-sided p=0.1747. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 5: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a food safety laboratory in South Harbor during a randomized pilot period has slope b=0.75, SEb=0.55, and n=41. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=0.750.55=1.364, df=39, two-sided p=0.1805. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 6: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a community bank in Midwest consortium during a winter readiness review has slope b=1.701, SEb=0.324, and n=49. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=1.7010.324=5.25, df=47, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 7: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a public high school in Central County during a regional benchmarking study has slope b=1.494, SEb=0.183, and n=43. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=1.4940.183=8.164, df=41, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 8: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a municipal water office in Pacific Northwest during a randomized pilot period has slope b=0.34, SEb=0.459, and n=30. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=0.340.459=0.741, df=28, two-sided p=0.465. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 9: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a university advising center in Great Lakes during a service-improvement study has slope b=1.264, SEb=0.294, and n=37. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=1.2640.294=4.299, df=35, two-sided p=0.0001. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 10: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a digital learning platform in Lakeside district during a weekday operations study has slope b=1.979, SEb=0.402, and n=37. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=1.9790.402=4.923, df=35, two-sided p=0. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 11: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a wildlife clinic in New England network during a baseline measurement week has slope b=1.518, SEb=0.471, and n=55. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=1.5180.471=3.223, df=53, two-sided p=0.0022. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 12: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a community college in Riverbend during a quarterly performance study has slope b=0.881, SEb=0.395, and n=52. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=0.8810.395=2.23, df=50, two-sided p=0.0302. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 13: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a regional manufacturer in Coastal Plains during a randomized pilot period has slope b=0.419, SEb=0.508, and n=27. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=0.4190.508=0.825, df=25, two-sided p=0.4173. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

FRQ set 14: Inference for a Regression Slope (Legacy/Enrichment)

Scenario. A regression sample at a university advising center in South Harbor during a two-month observation window has slope b=0.319, SEb=0.468, and n=51. Test H0:β=0, and identify the revised-2027 status.

  1. State the population parameter and hypotheses, including direction and group order.
  2. Verify the procedure conditions using evidence from the prompt.
  3. Compute the test statistic and p-value from the correct null model or expected counts.
  4. Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

t=b/SEb=0.3190.468=0.682, df=49, two-sided p=0.4987. The inference concerns the population slope β. Regression-slope inference is legacy/enrichment rather than required core content for the revised May 2027 AP Statistics exam.

Continue AP Statistics practice

AP Statistics Book 2027: Free Online Study Guide, Formulas, and Practice TestsOpen this practice pageAP Statistics Formula Sheet 2027: Formulas, Tables, and How to Use ItOpen this practice pageAP Statistics Exam Format 2027: Digital, 42 MCQs, and 4 FRQsOpen this practice pageAP Statistics Practice Test 2027: Full-Length Plan and AnswersOpen this practice pageAP Statistics Multiple-Choice Practice 2027: 42-Question StrategyOpen this practice pageAP Statistics FRQ Practice 2027: Four-Question Sets and SolutionsOpen this practice pageAP Statistics Exam Score Calculator 2027: Composite EstimateOpen this practice pageAP Statistics Calculator: Interactive Tools and Practice QuestionsOpen this practice pageAP Statistics Practice Questions by Topic: 2027 Five-Unit MapOpen this practice pageResiduals and Regression Diagnostics: Patterns and Influential PointsOpen this practice pageInference for a Regression Slope: Legacy AP Statistics GuideOpen this practice pageLeast-Squares Regression Line: Formula and InterpretationOpen this practice page

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Engr. Muhammad Yar Saqib author profile photo

Engr. Muhammad Yar Saqib

Engr. Muhammad Yar Saqib is an electrical engineer educated at the University of Bradford, United Kingdom, a writer and poet, and an Assistant Education Officer in the School Education Department, Punjab, serving since July 2017. He writes practical guides on statistics, SPSS, data analysis, mathematics and educational technology, with an emphasis on transparent methods, reproducible calculations and ethical learning support.

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