10. Hypothesis Testing for Two Samples

What conditions are necessary to use the dependent samples t-test for the mean of the differences for a population of paired data?

Test the claim about the mean of the differences for a population of paired data at the level of significance α. Assume the samples are random and dependent, and the populations are normally distributed.

Claim: μd≤0 , α=0.10, Sample statistics: d̄ =6.5, sd=9.54, n=16

Constructing Confidence Intervals for μd To construct a confidence interval for μd , use the inequality below.

Construct the indicated confidence interval for μd . Assume the populations are normally distributed.

[APPLET] Drug Testing A sleep disorder specialist wants to test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night. To do so, the specialist randomly selects 16 patients and records the number of hours of sleep each gets with and without the new drug. The table shows the results of the two-night study. Construct a 90% confidence interval for μd.

Performing a Sign Test In Exercises 7–22, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

[APPLET] Lower Back Pain A physician claims that lower back pain intensity scores will decrease after taking anti-inflammatory drugs. The table shows the lower back pain intensity scores for 12 patients before and after taking anti-inflammatory drugs for 8 weeks. At , is there enough evidence to support the physician’s claim? (Adapted from Archives of Internal Medicine)

Performing a Sign Test In Exercises 7–22, (c) find the test statistic,

[APPLET] Lower Back Pain A physician claims that lower back pain intensity scores will decrease after taking anti-inflammatory drugs. The table shows the lower back pain intensity scores for 12 patients before and after taking anti-inflammatory drugs for 8 weeks. At , is there enough evidence to support the physician’s claim? (Adapted from Archives of Internal Medicine)

Performing a Sign Test In Exercises 7–22, (b) find the critical value,

[APPLET] Lower Back Pain A physician claims that lower back pain intensity scores will decrease after taking anti-inflammatory drugs. The table shows the lower back pain intensity scores for 12 patients before and after taking anti-inflammatory drugs for 8 weeks. At , is there enough evidence to support the physician’s claim? (Adapted from Archives of Internal Medicine)

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha,

[APPLET] Lower Back Pain A physician claims that lower back pain intensity scores will decrease after taking anti-inflammatory drugs. The table shows the lower back pain intensity scores for 12 patients before and after taking anti-inflammatory drugs for 8 weeks. At , is there enough evidence to support the physician’s claim? (Adapted from Archives of Internal Medicine)

How do you know whether to use a Wilcoxon signed-rank test or a Wilcoxon rank sum test?

Performing a Sign Test In Exercises 7–22, (b) find the critical value,

[APPLET] SAT Scores A guidance counselor claims that students who take the SAT twice will improve their scores the second time that they take the SAT. The table shows both math SAT scores for 12 students who took the SAT twice. At α=0.01, can you support the guidance counselor’s claim?

Performing a Sign Test In Exercises 7–22, (c) find the test statistic,

[APPLET] SAT Scores A guidance counselor claims that students who take the SAT twice will improve their scores the second time that they take the SAT. The table shows both math SAT scores for 12 students who took the SAT twice. At α=0.01, can you support the guidance counselor’s claim?

Performing a Sign Test In Exercises 7–22, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

[APPLET] SAT Scores A guidance counselor claims that students who take the SAT twice will improve their scores the second time that they take the SAT. The table shows both math SAT scores for 12 students who took the SAT twice. At α=0.01, can you support the guidance counselor’s claim?

Performing a Wilcoxon Test In Exercises 3–8,

a. identify the claim and state H0 and Ha.

[APPLET] Calcium Supplements and Blood Pressure In a study testing the effects of calcium supplements on blood pressure in men, 12 men were randomly chosen and given a calcium supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At α = 0.01, can you reject the claim that there was no reduction in diastolic blood pressure? (Adapted from The Journal of the American Medical Association)

Performing a Wilcoxon Test In Exercises 3–8,

b. decide whether to use a Wilcoxon signed-rank test or a Wilcoxon rank sum test

[APPLET] Calcium Supplements and Blood Pressure In a study testing the effects of calcium supplements on blood pressure in men, 12 men were randomly chosen and given a calcium supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At α = 0.01, can you reject the claim that there was no reduction in diastolic blood pressure? (Adapted from The Journal of the American Medical Association)

Performing a Wilcoxon Test In Exercises 3–8,

c. find the critical value(s).

[APPLET] Calcium Supplements and Blood Pressure In a study testing the effects of calcium supplements on blood pressure in men, 12 men were randomly chosen and given a calcium supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At α = 0.01, can you reject the claim that there was no reduction in diastolic blood pressure? (Adapted from The Journal of the American Medical Association)

Performing a Wilcoxon Test In Exercises 3–8,

d. find the test statistic.

[APPLET] Calcium Supplements and Blood Pressure In a study testing the effects of calcium supplements on blood pressure in men, 12 men were randomly chosen and given a calcium supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At α = 0.01, can you reject the claim that there was no reduction in diastolic blood pressure? (Adapted from The Journal of the American Medical Association)