Find Upper and Lower Bounds on CI

Question

Do male and female servers work the same number of hours? A sample of 21 female servers worked an average of 33 hours per week, with a standard deviation of 2. A sample of 24 male servers worked an average of 39 hours per week, with a standard deviation of 3. Construct a 80% confidence interval for the mean difference in hours worked for male and female servers. You may assume that the populations are normal.

Answer 1

xbar1 = female sample mean 1 = 33

sd1 = female sample standard deviation 1 = 2

n1 = female

sample size 1 = 21

xbar2 = male sample mean 2 = 39

sd2 = male sample standard deviation 2= 3

n2 = male sample size 2 = 24

t-critical for 80% CI is t-score for upper alpha 0.10 and min(n1 -1 , n2 - 1) = 20 = 1.325

CI = (xbar2 - xbar1) +/- t-critical * sqrt(sd1^2/n1 + sd2^2/n1)

= (39 - 33) +/- 1.325 * sqrt(2^2/21 + 3^2/24)

you can complete the rest of the computations on your own