Worked solution P10-Easy-1. Select one-variable description, because it is defined for one quantitative variable and targets a population center or distribution. The matching reference expression is $$\overline{x}=\sum x_i/n.$$ Interpretation: The correct option will preserve the parameter and will describe shape, center, variability, and unusual features in context. Validity: Eliminate any choice that fails this requirement: check shape and unusual values before choosing resistant or nonresistant summaries. Error to reject: Choose one-proportion z interval because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-2. Select two-way table analysis, because it is defined for two categorical variables and targets conditional proportions and association. The matching reference expression is $$P(A\mid B)=P(A\cap B)/P(B).$$ Interpretation: The correct option will preserve the parameter and will compare conditional distributions without claiming causation. Validity: Eliminate any choice that fails this requirement: use the conditioning group's total as the denominator. Error to reject: Choose two-proportion z test because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-3. Select normal probability, because it is defined for one quantitative variable modeled as normal and targets a modeled tail or interval probability. The matching reference expression is $$z=(x-\mu )/\sigma .$$ Interpretation: The correct option will preserve the parameter and will translate standardized area back to the original context. Validity: Eliminate any choice that fails this requirement: justify the normal model before using normal areas. Error to reject: Choose one-sample t interval because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-4. Select binomial model, because it is defined for a fixed number of independent binary trials and targets a count of successes. The matching reference expression is $$P(X=k)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)p^k(1-p{)}^{n-k}.$$ Interpretation: The correct option will preserve the parameter and will interpret probability over repetitions of the full n-trial process. Validity: Eliminate any choice that fails this requirement: verify BINS, including constant p. Error to reject: Choose paired t test because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-5. Select sampling distribution for a mean, because it is defined for repeated random samples of size n and targets the behavior of sample means. The matching reference expression is $$S{E}_{\overline{X}}=\sigma /\sqrt{n}.$$ Interpretation: The correct option will preserve the parameter and will distinguish variation of sample means from variation of individuals. Validity: Eliminate any choice that fails this requirement: check independence and population shape or CLT support. Error to reject: Choose chi-square independence test because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-6. Select one-proportion z interval, because it is defined for one random sample with a binary response and targets a population proportion. The matching reference expression is $$\widehat{p}\pm z^{*}\sqrt{\widehat{p}(1-\widehat{p})/n}.$$ Interpretation: The correct option will preserve the parameter and will state confidence as a property of the interval method. Validity: Eliminate any choice that fails this requirement: check randomization, independence, and large observed counts. Error to reject: Choose least-squares regression because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-7. Select two-proportion z test, because it is defined for two independent groups with binary responses and targets equality of two population proportions. The matching reference expression is $$z=({\widehat{p}}_1-{\widehat{p}}_2)/S{E}_0.$$ Interpretation: The correct option will preserve the parameter and will conclude about evidence for a population difference. Validity: Eliminate any choice that fails this requirement: pool only under the equal-proportions null. Error to reject: Choose randomized experiment because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-8. Select one-sample t interval, because it is defined for one quantitative sample with unknown sigma and targets a population mean. The matching reference expression is $$\overline{x}\pm t^{*}s/\sqrt{n}.$$ Interpretation: The correct option will preserve the parameter and will report the interval in measurement units. Validity: Eliminate any choice that fails this requirement: check randomization, independence, and robustness to shape. Error to reject: Choose one-variable description because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-9. Select paired t test, because it is defined for matched or before-after quantitative measurements and targets a population mean difference. The matching reference expression is $$t=\overline{d}/(s_d/\sqrt{n}).$$ Interpretation: The correct option will preserve the parameter and will conclude about the mean within-pair change. Validity: Eliminate any choice that fails this requirement: analyze independent pair differences. Error to reject: Choose two-way table analysis because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-10. Select chi-square independence test, because it is defined for one population classified by two categorical variables and targets association between the variables. The matching reference expression is $${\chi }^2=\sum (O-E{)}^2/E.$$ Interpretation: The correct option will preserve the parameter and will conclude about association rather than causation. Validity: Eliminate any choice that fails this requirement: check randomization, independent observations, and expected counts. Error to reject: Choose normal probability because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-11. Select least-squares regression, because it is defined for two quantitative variables and targets a linear predictive association. The matching reference expression is $$\widehat{y}=a+bx.$$ Interpretation: The correct option will preserve the parameter and will interpret slope and predictions within the observed x range. Validity: Eliminate any choice that fails this requirement: inspect form, residual pattern, and influential points. Error to reject: Choose binomial model because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-12. Select randomized experiment, because it is defined for experimental units assigned to treatments and targets a treatment effect. The matching reference expression is $$\text{effect estimate}={\overline{x}}_T-{\overline{x}}_C.$$ Interpretation: The correct option will preserve the parameter and will support causation while limiting population generalization to the sampling design. Validity: Eliminate any choice that fails this requirement: use random assignment, comparison, control, and replication. Error to reject: Choose sampling distribution for a mean because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-13. Select one-variable description, because it is defined for one quantitative variable and targets a population center or distribution. The matching reference expression is $$\overline{x}=\sum x_i/n.$$ Interpretation: The correct option will preserve the parameter and will describe shape, center, variability, and unusual features in context. Validity: Eliminate any choice that fails this requirement: check shape and unusual values before choosing resistant or nonresistant summaries. Error to reject: Choose one-proportion z interval because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Easy-14. Select two-way table analysis, because it is defined for two categorical variables and targets conditional proportions and association. The matching reference expression is $$P(A\mid B)=P(A\cap B)/P(B).$$ Interpretation: The correct option will preserve the parameter and will compare conditional distributions without claiming causation. Validity: Eliminate any choice that fails this requirement: use the conditioning group's total as the denominator. Error to reject: Choose two-proportion z test because all statistical procedures can be substituted when they produce a calculator result.

Worked solution P10-Tough-1. Use one-variable description; one-proportion z interval addresses a population proportion under one random sample with a binary response, which does not match this prompt. The selected setup is $$\overline{x}=\sum x_i/n.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will describe shape, center, variability, and unusual features in context without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: check shape and unusual values before choosing resistant or nonresistant summaries. Error to reject: Use one-proportion z interval after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-2. Use two-way table analysis; two-proportion z test addresses equality of two population proportions under two independent groups with binary responses, which does not match this prompt. The selected setup is $$P(A\mid B)=P(A\cap B)/P(B).$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will compare conditional distributions without claiming causation without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: use the conditioning group's total as the denominator. Error to reject: Use two-proportion z test after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-3. Use normal probability; one-sample t interval addresses a population mean under one quantitative sample with unknown sigma, which does not match this prompt. The selected setup is $$z=(x-\mu )/\sigma .$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will translate standardized area back to the original context without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: justify the normal model before using normal areas. Error to reject: Use one-sample t interval after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-4. Use binomial model; paired t test addresses a population mean difference under matched or before-after quantitative measurements, which does not match this prompt. The selected setup is $$P(X=k)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)p^k(1-p{)}^{n-k}.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will interpret probability over repetitions of the full n-trial process without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: verify BINS, including constant p. Error to reject: Use paired t test after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-5. Use sampling distribution for a mean; chi-square independence test addresses association between the variables under one population classified by two categorical variables, which does not match this prompt. The selected setup is $$S{E}_{\overline{X}}=\sigma /\sqrt{n}.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will distinguish variation of sample means from variation of individuals without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: check independence and population shape or CLT support. Error to reject: Use chi-square independence test after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-6. Use one-proportion z interval; least-squares regression addresses a linear predictive association under two quantitative variables, which does not match this prompt. The selected setup is $$\widehat{p}\pm z^{*}\sqrt{\widehat{p}(1-\widehat{p})/n}.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will state confidence as a property of the interval method without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: check randomization, independence, and large observed counts. Error to reject: Use least-squares regression after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-7. Use two-proportion z test; randomized experiment addresses a treatment effect under experimental units assigned to treatments, which does not match this prompt. The selected setup is $$z=({\widehat{p}}_1-{\widehat{p}}_2)/S{E}_0.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will conclude about evidence for a population difference without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: pool only under the equal-proportions null. Error to reject: Use randomized experiment after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-8. Use one-sample t interval; one-variable description addresses a population center or distribution under one quantitative variable, which does not match this prompt. The selected setup is $$\overline{x}\pm t^{*}s/\sqrt{n}.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will report the interval in measurement units without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: check randomization, independence, and robustness to shape. Error to reject: Use one-variable description after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-9. Use paired t test; two-way table analysis addresses conditional proportions and association under two categorical variables, which does not match this prompt. The selected setup is $$t=\overline{d}/(s_d/\sqrt{n}).$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will conclude about the mean within-pair change without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: analyze independent pair differences. Error to reject: Use two-way table analysis after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-10. Use chi-square independence test; normal probability addresses a modeled tail or interval probability under one quantitative variable modeled as normal, which does not match this prompt. The selected setup is $${\chi }^2=\sum (O-E{)}^2/E.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will conclude about association rather than causation without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: check randomization, independent observations, and expected counts. Error to reject: Use normal probability after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-11. Use least-squares regression; binomial model addresses a count of successes under a fixed number of independent binary trials, which does not match this prompt. The selected setup is $$\widehat{y}=a+bx.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will interpret slope and predictions within the observed x range without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: inspect form, residual pattern, and influential points. Error to reject: Use binomial model after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-12. Use randomized experiment; sampling distribution for a mean addresses the behavior of sample means under repeated random samples of size n, which does not match this prompt. The selected setup is $$\text{effect estimate}={\overline{x}}_T-{\overline{x}}_C.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will support causation while limiting population generalization to the sampling design without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: use random assignment, comparison, control, and replication. Error to reject: Use sampling distribution for a mean after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-13. Use one-variable description; one-proportion z interval addresses a population proportion under one random sample with a binary response, which does not match this prompt. The selected setup is $$\overline{x}=\sum x_i/n.$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will describe shape, center, variability, and unusual features in context without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: check shape and unusual values before choosing resistant or nonresistant summaries. Error to reject: Use one-proportion z interval after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Tough-14. Use two-way table analysis; two-proportion z test addresses equality of two population proportions under two independent groups with binary responses, which does not match this prompt. The selected setup is $$P(A\mid B)=P(A\cap B)/P(B).$$ A formula match is necessary but must follow the data-structure match. Interpretation: The option is complete only if it will compare conditional distributions without claiming causation without changing the order, units, or population named in the question. Validity: Verify the operative condition rather than a memorized generic list: use the conditioning group's total as the denominator. Error to reject: Use two-proportion z test after changing the target parameter so the available calculator menu appears to fit.

Worked solution P10-Toughest-1. Choose the option that uses one-variable description, targets a population center or distribution, verifies check shape and unusual values before choosing resistant or nonresistant summaries, and then will describe shape, center, variability, and unusual features in context. The numerical reasoning must be organized by $$\overline{x}=\sum x_i/n.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-2. Choose the option that uses two-way table analysis, targets conditional proportions and association, verifies use the conditioning group's total as the denominator, and then will compare conditional distributions without claiming causation. The numerical reasoning must be organized by $$P(A\mid B)=P(A\cap B)/P(B).$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-3. Choose the option that uses normal probability, targets a modeled tail or interval probability, verifies justify the normal model before using normal areas, and then will translate standardized area back to the original context. The numerical reasoning must be organized by $$z=(x-\mu )/\sigma .$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-4. Choose the option that uses binomial model, targets a count of successes, verifies verify BINS, including constant p, and then will interpret probability over repetitions of the full n-trial process. The numerical reasoning must be organized by $$P(X=k)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)p^k(1-p{)}^{n-k}.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-5. Choose the option that uses sampling distribution for a mean, targets the behavior of sample means, verifies check independence and population shape or CLT support, and then will distinguish variation of sample means from variation of individuals. The numerical reasoning must be organized by $$S{E}_{\overline{X}}=\sigma /\sqrt{n}.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-6. Choose the option that uses one-proportion z interval, targets a population proportion, verifies check randomization, independence, and large observed counts, and then will state confidence as a property of the interval method. The numerical reasoning must be organized by $$\widehat{p}\pm z^{*}\sqrt{\widehat{p}(1-\widehat{p})/n}.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-7. Choose the option that uses two-proportion z test, targets equality of two population proportions, verifies pool only under the equal-proportions null, and then will conclude about evidence for a population difference. The numerical reasoning must be organized by $$z=({\widehat{p}}_1-{\widehat{p}}_2)/S{E}_0.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-8. Choose the option that uses one-sample t interval, targets a population mean, verifies check randomization, independence, and robustness to shape, and then will report the interval in measurement units. The numerical reasoning must be organized by $$\overline{x}\pm t^{*}s/\sqrt{n}.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-9. Choose the option that uses paired t test, targets a population mean difference, verifies analyze independent pair differences, and then will conclude about the mean within-pair change. The numerical reasoning must be organized by $$t=\overline{d}/(s_d/\sqrt{n}).$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-10. Choose the option that uses chi-square independence test, targets association between the variables, verifies check randomization, independent observations, and expected counts, and then will conclude about association rather than causation. The numerical reasoning must be organized by $${\chi }^2=\sum (O-E{)}^2/E.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-11. Choose the option that uses least-squares regression, targets a linear predictive association, verifies inspect form, residual pattern, and influential points, and then will interpret slope and predictions within the observed x range. The numerical reasoning must be organized by $$\widehat{y}=a+bx.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-12. Choose the option that uses randomized experiment, targets a treatment effect, verifies use random assignment, comparison, control, and replication, and then will support causation while limiting population generalization to the sampling design. The numerical reasoning must be organized by $$\text{effect estimate}={\overline{x}}_T-{\overline{x}}_C.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-13. Choose the option that uses one-variable description, targets a population center or distribution, verifies check shape and unusual values before choosing resistant or nonresistant summaries, and then will describe shape, center, variability, and unusual features in context. The numerical reasoning must be organized by $$\overline{x}=\sum x_i/n.$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.

Worked solution P10-Toughest-14. Choose the option that uses two-way table analysis, targets conditional proportions and association, verifies use the conditioning group's total as the denominator, and then will compare conditional distributions without claiming causation. The numerical reasoning must be organized by $$P(A\mid B)=P(A\cap B)/P(B).$$ Sign, denominator, tail direction, and subtraction order must agree with the parameter. Interpretation: The final choice must distinguish association from causation, sample evidence from population truth, and statistical significance from practical importance whenever those distinctions are relevant. Validity: Use information about random sampling, random assignment, independence, shape, counts, or residuals only for the inferential claim that each feature actually supports. Error to reject: Select the option with the smallest displayed p-value even when it uses a mismatched procedure, ignores the design, or answers a different parameter question.