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, 50 had a Master\'s degree and 75 had a Bachelor\'s Degree only. The average hourly rate for those with a Master\'s was $43.735 (SD = $4.138). Among the graduates with a Bachelor\'s degree, the average hourly rate was $24.985 (SD = $7.717). You use this information to calculate a 95% confidence interval for the difference in mean hourly wage of (16.391, 21.109). Of the following statements, what is the best interpretation of this interval?

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

b) We are 95% 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 16.391 and 21.109

c) We are 95% 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 16.391 and 21.109

d) We are 95% 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 16.391 and 21.109

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 16.391 and 21.109

[Please explain]

Solution

95% 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 16.391 and 21.109