Question

A student believed that students in a Health Sciences program at his college studied, on average, more than students in other programs. He decided to assess whether this was true by collecting data on the typical number of hours per week that students studied during the semester. He collected data from a random sample of students. The table below summarizes the results. n Sample Mean Sample Standard Deviation Health Sciences 42 24.3 5.65 Other Programs 35 22.0 8.35 Let µ1 be mean number of hours per week that Health Sciences students study, and let µ2 be the mean number of hours per week that students in other programs study. If we assume that the population means are the same, µ1 = µ2 , what is the T-test statistic of the observed difference in sample means? Round to two decimal places.

Answer 1

For Sample 1 :

x̅1 = 24.3, s1 = 5.65, n1 = 42

For Sample 2 :

x̅2 = 22, s2 = 8.35, n2 = 35

Test statistic:

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2) = (24.3 - 22)/√(5.65²/42 + 8.35²/35) = 1.39