Student t Distribution Problem

Question

Question/Problem:

Data Set 1 in Appendix B lists the white blood cell counts (1000 cells/µL) of 40 randomly selected women. The mean of those 40 values is 7.15 and the standard deviation is 2.28. Construct a 90% confidence interval estimate of the mean white blood cell count for the population of women. Does the confidence interval also serve as an estimate of the mean white blood cell count of men?

Please help me step by step. Thank you!

Answer 1

Confidence Interval = [x-t_α/2*(s/√n), x+t_α/2*(s/√n)] with degree of freedom 40-1=39

= [7.15-1.684*2.28/√40, 7.15+1.684*2.28/√40]

= [6.5429, 7.7571]