In: Statistics and Probability
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."
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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
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