When comparing two population means using data that are gathered from a matched pairs experiment, the test statistic for is Student's t distributed, with degrees of freedom, provided that the differences are normally distributed.

Question

When comparing two population means using data that are gathered from a matched pairs experiment, the test statistic for  is Student's t distributed, with  degrees of freedom, provided that the differences are normally distributed.

Quizplus · Accepted Answer

When comparing two population means using data that are gathered from a matched pairs experiment, the differences between the pairs of observations are used. If the sample size is small (less than 30) and the population standard deviation is unknown, Student's t-test is used. The test statistic for a paired t-test is given by:

t = (sample mean of differences - hypothesized difference)/(standard error of the mean difference)

Under the null hypothesis that the means of the two populations are equal, the test statistic follows a Student's t distribution with n-1 degrees of freedom, where n is the number of pairs of observations. Therefore, the statement is true that the test statistic for a matched pairs experiment is Student's t distributed with n-1 degrees of freedom, provided that the differences are normally distributed.

When Comparing Two Population Means Using Data That Are Gathered