Problem Details A large firm employing tens of thousands of workers has been acc

Question

Problem Details

A large firm employing tens of thousands of workers has been accused of discriminating against its female managers. The accusation is based on a random sample of 100 managers. The president of the firm points out that the company has a strict policy of equal pay for equal work. He disputes the claim of discrimination and contends that if a difference exists, it is due to other variables. Accordingly, in addition to the salary and gender information for the 100 managers, he has provided you and your team with the number of years of education and the number of years of experience for each of the 100 managers in the sample.

Requirements

1.Perform a preliminary statistical test to determine if there is a significant difference in average salary for the male and female managers. If a significant difference is found, …

2.Use regression analysis to find the best model to explain the variability in salary. Of course, the president hopes that your model does not include Gender as a significant predictor, but you must report what the model reveals, even if it turns out to be not what the president hopes for.

A thorough analysis will include appropriate preliminary graphs, correlations, and data summary. A thorough analysis will include investigation of more than one regression model.

Summarize your findings from all models investigated in a table similar to the one found on slide 19 of the Multiple Regression Part II notes. This table should be included in your REPORT section.

A thorough analysis will include verification of required data conditions.

A thorough analysis will include appropriate tests of significance. Make recommendations in your report for additional information that you think shed additional light on the salary differences

Data

Salary Education Experience Gender 142760 18 19 male 125360 15 21 male 77030 15 14 male 158960 14 26 male 85470 15 8 male 77290 12 14 female 81640 15 12 male 101750 14 8 female 145110 13 23 male 69640 15 11 female 99090 16 17 female 101400 12 17 female 61260 16 16 male 30200 16 1 female 100250 16 14 female 93830 17 14 male 90990 15 17 male 88350 17 9 female 97480 17 14 male 106830 14 15 female 47400 16 6 female 68690 15 16 male 131560 17 20 male 110660 15 20 male 80320 15 16 male 70160 18 17 female 109680 18 21 male 97790 16 14 male 57960 16 11 female 36860 12 10 male 56590 15 3 female 68620 17 15 male 93390 17 11 male 86010 14 15 male 132010 17 23 male 91450 13 18 male 70030 18 12 female 74810 13 19 male 83160 15 14 female 75490 15 12 female 114970 17 19 male 62260 15 12 male 50690 14 11 female 116930 17 17 male 57100 14 11 female 93090 14 14 male 76820 15 16 male 91850 11 14 male 126750 16 20 male 90070 16 9 male 80090 15 11 female 97440 14 16 male 63330 12 10 female 120580 15 19 male 100930 14 9 female 20860 11 6 male 82430 17 10 male 92840 14 22 male 89050 16 12 female 129790 17 20 female 81760 15 10 male 66380 15 13 female 175760 15 36 male 46690 19 8 female 139260 15 24 male 165400 16 30 male 115500 14 21 male 94470 14 23 female 87320 16 16 female 105750 14 19 male 105570 17 24 male 98050 16 18 female 92630 15 15 male 80520 16 16 female 91560 16 15 female 79290 14 17 male 99710 14 18 female 113920 15 23 male 44760 14 11 female 82100 16 16 male 99680 15 19 male 87920 15 15 male 79100 16 12 male 122940 16 22 male 119470 17 22 male 47880 14 5 male 31240 18 5 female 134540 16 22 male 84340 13 19 male 50620 13 6 64540 16 10 male 83430 14 14 female 109360 17 19 male 67670 18 11 female 98940 15 13 male 89150 18 10 female 92720 15 14 male 68670 14 15 male 57040 15 10 female 67920 16 15 male

Explanation / Answer

as per company policies I am answering question 1 only

Ho: there is no significant difference in the mean salary between males and females

H1: there is a significant difference in the mean salary between males and females

T =
= (Xbar1-Xbar2)/sqrt(s1^2/n1 + s2^2/n2)
= (97799.8387096774-76880)/sqrt(13908754.44+13898956.01)
3.9671

df=
(s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1))
(13908754.44+13898956.01)^2/(13908754.44^2/(62-1) + 13898956.01^2/(37-1))
244

alpha= 0.05

t(a/2, df) =t(0.05/2,244) =F.INV.2T(0.05,244) = 1.970

p-value
2*(1-P(T<|t|)
2*(1-P(T<abs(3.9671))
T.DIST.2T(abs(3.9671),244)
9.57831E-05

Since P-value is less than 5%, I reject the null hypothesis at 5% level of significance and conclude that there is a significant difference in the mean salary between males and females

Experimental Control n= 62 37 COUNT mean= 97799.8 76880.0 AVERAGE s= 29365.7 22677.3 STDEV s^2/n 13908754.44 13898956.01

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