Worked solution P59-Easy-1. The t interval is (69.084, 77.116). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.10\pm 4.016.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Easy-2. The paired t interval is (1.021, 4.779). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.90\pm 1.879.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Easy-3. The t interval is (69.544, 77.656). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.60\pm 4.056.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Easy-4. The paired t interval is (0.829, 4.771). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.80\pm 1.971.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Easy-5. The t interval is (69.931, 76.669). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.30\pm 3.369.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Easy-6. The paired t interval is (1.361, 5.039). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=3.20\pm 1.839.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Easy-7. The t interval is (69.418, 76.382). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=72.90\pm 3.482.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Easy-8. The paired t interval is (0.494, 4.106). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.30\pm 1.806.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Easy-9. The t interval is (67.101, 73.299). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=70.20\pm 3.099.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Easy-10. The paired t interval is (1.003, 4.397). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.70\pm 1.697.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Easy-11. The t interval is (67.151, 74.249). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=70.70\pm 3.549.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Easy-12. The paired t interval is (0.521, 4.279). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.40\pm 1.879.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Easy-13. The t interval is (67.482, 73.518). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=70.50\pm 3.018.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Easy-14. The paired t interval is (0.559, 4.041). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.30\pm 1.741.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Easy-15. The t interval is (70.305, 75.894). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.10\pm 2.794.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Easy-16. The paired t interval is (0.861, 4.539). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.70\pm 1.839.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Easy-17. The t interval is (69.888, 77.312). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.60\pm 3.712.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Easy-18. The paired t interval is (1.762, 5.038). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=3.40\pm 1.638.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Tough-1. The t interval is (67.475, 76.125). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=71.80\pm 4.325.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Tough-2. The paired t interval is (0.314, 3.686). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.00\pm 1.686.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Tough-3. The t interval is (70.620, 77.380). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=74.00\pm 3.380.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Tough-4. The paired t interval is (0.396, 3.604). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.00\pm 1.604.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Tough-5. The t interval is (66.812, 73.388). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=70.10\pm 3.288.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Tough-6. The paired t interval is (0.580, 3.820). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.20\pm 1.620.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Tough-7. The t interval is (66.540, 73.660). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=70.10\pm 3.560.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Tough-8. The paired t interval is (1.762, 5.038). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=3.40\pm 1.638.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Tough-9. The t interval is (70.972, 78.228). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=74.60\pm 3.628.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Tough-10. The paired t interval is (0.585, 3.415). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.00\pm 1.415.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Tough-11. The t interval is (67.024, 73.976). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=70.50\pm 3.476.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Tough-12. The paired t interval is (1.177, 5.223). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=3.20\pm 2.023.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Tough-13. The t interval is (70.289, 76.111). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.20\pm 2.911.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Tough-14. The paired t interval is (0.384, 4.416). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.40\pm 2.016.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Tough-15. The t interval is (68.026, 74.374). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=71.20\pm 3.174.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Tough-16. The paired t interval is (1.636, 4.964). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=3.30\pm 1.664.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Tough-17. The t interval is (67.343, 75.457). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=71.40\pm 4.057.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Tough-18. The paired t interval is (0.494, 4.106). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.30\pm 1.806.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Toughest-1. The t interval is (67.419, 75.981). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=71.70\pm 4.281.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Toughest-2. The paired t interval is (0.417, 3.983). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.20\pm 1.783.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Toughest-3. The t interval is (66.793, 73.807). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=70.30\pm 3.507.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Toughest-4. The paired t interval is (1.275, 5.125). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=3.20\pm 1.925.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Toughest-5. The t interval is (70.168, 77.232). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.70\pm 3.532.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Toughest-6. The paired t interval is (1.524, 4.676). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=3.10\pm 1.576.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Toughest-7. The t interval is (71.053, 77.547). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=74.30\pm 3.247.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Toughest-8. The paired t interval is (1.146, 4.254). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.70\pm 1.554.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Toughest-9. The t interval is (67.101, 73.299). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=70.20\pm 3.099.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Toughest-10. The paired t interval is (0.764, 3.836). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.30\pm 1.536.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Toughest-11. The t interval is (70.643, 77.157). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.90\pm 3.257.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Toughest-12. The paired t interval is (0.780, 5.020). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.90\pm 2.120.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Toughest-13. The t interval is (69.869, 76.331). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.10\pm 3.231.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Toughest-14. The paired t interval is (0.504, 3.896). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.20\pm 1.696.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Toughest-15. The t interval is (68.830, 74.971). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=71.90\pm 3.071.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Toughest-16. The paired t interval is (0.967, 4.033). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.50\pm 1.533.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.

Worked solution P59-Toughest-17. The t interval is (69.945, 77.455). $$\overline{x}\pm t^{*}\frac{s}{\sqrt{n}}=73.70\pm 3.755.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Use a random sample or randomized design, independence, and a population shape or sample size that makes the t procedure reliable. Error to reject: Use t rather than z when sigma is unknown and sample standard deviation s estimates it.

Worked solution P59-Toughest-18. The paired t interval is (0.494, 4.106). $$\overline{d}\pm t^{*}\frac{s_d}{\sqrt{n}}=2.30\pm 1.806.$$ Interpretation: The interval estimates a population mean in the original measurement units and must name the represented population. Validity: Analyze the within-pair differences, check randomization and independence of pairs, and inspect the difference distribution for strong skew or outliers. Error to reject: Do not run an independent two-sample interval on paired measurements; pairing changes the observational unit to a difference.