10. Hypothesis Testing for Two Samples

A personal trainer is studying whether a new stretching routine improves flexibility. She records the forward reach (in cm) of 6 clients before and after a 4-week program. Calculate the difference (after - before) for each client, the mean difference, and standard deviation.

Construct a 95% confidence interval for the mean difference of the population given the following information. Would you reject or fail to reject the claim that there is no difference in the mean?

$\bar{d}=-0.728$

$s_d=1.34$

$n=10$

When testing the difference of means for paired data, which of the following is the correct null hypothesis?

Which of the following is an example of a dependent sample suitable for analysis with the $t$-test?