10. Hypothesis Testing for Two Samples

Which of the following situations is a matched pairs $t$ test not an appropriate way to analyze?

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?

Which of the following scenarios is most likely to involve dependent samples ($\mathrm{matched} \mathrm{pairs}$)?

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=0.05 , Sample statistics: d̄ =1.5 , sd=3.2 , n=14

In Exercises 1–4, classify the two samples as independent or dependent and justify your answer.

Sample 1: The retail prices of 20 motorcycles

Sample 2: The retail prices of 20 minivans

Two samples are $————————————$ if the sample values are paired.

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.