Use the Following Information for Questions

Multiple Choice

Use the following information for questions:
High school students can be categorized into two groups by the amount of activities they are involved in. Let group 1 consist of all high school students who are very involved in sports and other activities and group 2 consist of all high school students who aren't. The distributions of GPAs in both groups are approximately normal. The mean and standard deviation for group 1 are 2.9 and 0.4, respectively. The mean and standard deviation for group 2 are 2.7 and 0.5, respectively. Independent random samples of 50 high school students are to be selected from both groups (for a total of 100 students) .
-If the sample mean GPA is to be calculated for both groups and we calculate the difference as involved in activities - not so involved in activities, what is the standard deviation of the sampling distribution of the difference in sample means?

A) 0.0082
B) 0.0905
C) 0.18
D) 0.45