Ten couples are participating in a small study on cholesterol.Neither the man nor the woman in each couple is known to have any problems with high cholesterol.The researcher conducting the study wishes to use the sign test for matched pairs to determine if there is evidence that the cholesterol level for the husband tends to be higher than the cholesterol level for the wife.The cholesterol measurements for the 10 couples are given below. What are the hypotheses the researcher wishes to test? A)H₀: $\mu$ = 0 versus H_a: $\mu$ 0,where $\mu$ = the mean of the differences in cholesterol levels (husband - wife)for all couples without cholesterol problems B)H₀: p = ¹/₂ versus H_a: p$\neq$¹/₂,where p = the proportion of cholesterol levels of the husband that are higher than those of the wife C)H₀: p = ¹/₂ versus H_a: p 0,where the differences for which the median is calculated are measured as husband - wife

Question

Ten couples are participating in a small study on cholesterol.Neither the man nor the woman in each couple is known to have any problems with high cholesterol.The researcher conducting the study wishes to use the sign test for matched pairs to determine if there is evidence that the cholesterol level for the husband tends to be higher than the cholesterol level for the wife.The cholesterol measurements for the 10 couples are given below. What are the hypotheses the researcher wishes to test? A)H₀: $\mu$ = 0 versus H_a: $\mu$> 0,where $\mu$ = the mean of the differences in cholesterol levels (husband - wife)for all couples without cholesterol problems B)H₀: p = ¹/₂ versus H_a: p$\neq$¹/₂,where p = the proportion of cholesterol levels of the husband that are higher than those of the wife C)H₀: p = ¹/₂ versus H_a: p < ¹/₂,where p = the proportion of cholesterol levels of the husband that are higher than those of the wife D)H₀: population median = 0 versus H_a: population median > 0,where the differences for which the median is calculated are measured as husband - wife

Quizplus · Accepted Answer

The researcher wishes to use the sign test for matched pairs, which compares the median differences in cholesterol levels between husbands and wives. Therefore, the hypotheses should be written in terms of the population median. Choice D is the only option that presents the hypotheses in this way. Choices A and B refer to the mean and proportion, respectively, which are not appropriate for the sign test. Choice C is similar to choice B but has a less than sign, which is not appropriate for the sign test.

Ten Couples Are Participating in a Small Study on Cholesterol μ\muμ

Ten Couples Are Participating in a Small Study on Cholesterol $\mu$