Comparing Data Sets HW Question 2

Can’t seem to get the correct calculations for the second problem. I’ve tried squaring the std. deviations and not squaring them-- neither way worked.

Here’s what I’ve been doing.

Ex:
“Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the .05 significance level.The sample consisted of 65 night students, with a sample mean GPA of 2.07 and a standard deviation of 0.07, and 70 day students, with a sample mean GPA of 2.05 and a standard deviation of 0.06.”

Test Statistic Calculation:
SE =sqrt((0.07/65)+(0.06/70)) = 0.04397802

(2.05-2.07)/0.04397802 = -0.4547726

Critical Value Calculation:

pt(-0.4547726,64)
[1] 0.3254059

Any help?

Well, certainly you should be squareing the standard deviations to get

SE =sqrt(0.07^2/65+0.06^2/70) = 0.01126

We then get a test-statistic of

(2.07-2.05)/0.01126 = 1.776.

Note that the difference comes in the order stated in the problem. Finally, we find the critical value using a command like:

qt(0.95,64)

# Out: 
# [1] 1.669013