A university is comparing the hourly wages of students of th

A university is comparing the hourly wages of students of their university who completed a Master\'s Degree to students who only completed a Bachelor\'s Degree. Of the students surveyed, 56 had a Master\'s degree and 65 had a Bachelor\'s Degree only. The average hourly rate for those with a Master\'s was $46.806 (SD = $3.855). Among the graduates with a Bachelor\'s degree, the average hourly rate was $21.024 (SD = $8.92). You use this information to calculate a 90% confidence interval for the difference in mean hourly wage of (23.651, 27.913). Of the following statements, what is the best interpretation of this interval?

a) We are 90% sure that the difference in average hourly wage of all nationwide graduates with a Master\'s degree and all nationwide graduates with a Bachelor\'s degree is between 23.651 and 27.913

b) We are 90% confident that the difference between the average hourly wage of all their graduates with a Master\'s degree and all their graduates with a Bachelor\'s degree is between 23.651 and 27.913

c) We are 90% confident that the difference between the average hourly wage of all their graduates with a Master\'s degree and all their graduates with a Bachelor\'s degree surveyed is between 23.651 and 27.913

d) We do not know the population means so we do not have enough information to make an interpretation

e) We are certain that the difference between the average hourly wage of all graduates with a Master\'s degree and all graduates with a Bachelor\'s degree is between 23.651 and 27.913

[Please explain]

Solution

a) We are 90% sure that the difference in average hourly wage of all nationwide graduates with a Master\'s degree and all nationwide graduates with a Bachelor\'s degree is between 23.651 and 27.913

that is the answer because the confidence interval is for the population, not for the sample

we are calculating a interval where the true mean will be in that interval with 90% of confident