Question

A Houston- area labor economist wants to see if the difference between men and woman when it comes to the mean years of experience for General Manager. After sending out a survey to restaurants in the Houston area, she obtained the following data:

Group                                      Mean                         Standard Deviation                        n

Men (Group 1)                          14.1                                     3.5                                      199

Women (Group 2)                      9.6                                      2.6                                      44

a.) Calculate a 99% confidence interval for the difference in mean of experience between men and women who are general managers. Use the fact that the degrees of freedom v=82

b.) Interpet the interval you calculated in (a) in the contact of the problem statement, by filling out the blanks below

The Research can be 95% confident that the __________________________ between _____________ and _____ is between __ and ______________.

c.) Using your answers (b), can the researcher conclude that the two of managers differ in mean years of experience? Yes or No?

                                    Assistant Manager                      General Manager                    Other                  Total

Men                                      340                                                 199                                   146                      685

Women                                168                                                    44                                     14                       226             

Answer 1

Given
X1 bar	14.1	X2 bar	9.6
S1	3.5	S2	2.6
n1	199	n2	44

X1 bar - X2 bar = 14.1-9.6 = 4.5

Unequal variance
2.63712341	T.INV.2T(D1,D2)
5.723335806	(X1 bar-X2 bar )+tc*SQRT(S1^2/n1 + S2^2/n2)
3.276664194	(X1 bar-X2 bar )-tc*SQRT(S1^2/n1 + S2^2/n2)

95% CI values in 99% CI

The Research can be 95% confident that the population mean difference between men and woman is between 3.58 and 5.42

Yes, above CI does not have 0, so, we can conclude that the two of managers differ in mean years of experience