Question

In: Statistics and Probability

Suppose the following data were collected relating CEO salary to years of experience and gender. Use...

Suppose the following data were collected relating CEO salary to years of experience and gender. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average male CEOs have higher salaries than female CEOs at the 0.050.05 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."

Copy Data

CEO Salaries
Salary Experience Male (1 if male, 0 if female)
103686.94103686.94 1212 11
103269.97103269.97 2424 00
118771.02118771.02 1717 11
95772.1695772.16 33 00
147548.23147548.23 2828 11
99526.5799526.57 1414 00
71602.3671602.36 22 11
97535.8597535.85 1010 11
90890.2090890.20 99 11
96219.9096219.90 55 00
103963.60103963.60 2727 00
100308.28100308.28 1616 00
92858.1892858.18 11 00
101245.05101245.05 1010 11
99042.1399042.13 1212 00
80504.4480504.44 66 11
103519.53103519.53 2222 00
95526.7095526.70 1010 11
98473.2898473.28 1111 00
119389.22119389.22 1717 11

Answer(How to Enter)

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SALARYi=SALARYi= b0  ++ b1 EXPERIENCEiEXPERIENCEi ++ b2 MALEi+eiMALEi+ei  There is not enough evidence

Solutions

Expert Solution

using minitab>stat>basic stat>tw sa,mpe lt

we have

Two-Sample T-Test and CI: Salary, Male (1 if male, 0 if female)

Two-sample T for Salary

Male (1 if
male, 0 if
female) N Mean StDev SE Mean
0 10 99295 3660 1157
1 10 102670 21676 6854


Difference = μ (0) - μ (1)
Estimate for difference: -3375
95% lower bound for difference: -15429
T-Test of difference = 0 (vs <): T-Value = -0.49 P-Value = 0.317 DF = 18
Both use Pooled StDev = 15544.0543

yes , there is enough evidence to support the claim that on average male CEOs have higher salaries than female CEOs .

using excel>data>data analysis >regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.74417
R Square 0.55379
Adjusted R Square 0.501294
Standard Error 10754.01
Observations 20
ANOVA
df SS MS F Significance F
Regression 2 2.44E+09 1.22E+09 10.54931 0.00105
Residual 17 1.97E+09 1.16E+08
Total 19 4.41E+09
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 80121.68 5422.689 14.77527 3.93E-11 68680.81 91562.56 68680.81 91562.56
Experience 1420.272 312.8758 4.539412 0.00029 760.162 2080.383 760.162 2080.383
Male (1 if male, 0 if female) 5363.022 4829.246 1.11053 0.282232 -4825.8 15551.84 -4825.8 15551.84

the regression equation is

SALARYi= 80121.68 + 1420.272 EXPERIENCEi+ 5363.022 MALEi+ei


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