Question 1. Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean.
(Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-test and making the second variable = Ho value)
Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female average salaries?
Males Females
Ho: Mean salary = 45 Ho: Mean salary = 45
Ha: Mean salary =/= 45 Ha: Mean salary =/= 45
Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome - we are tricking Excel into doing a one sample test for us.
| |
Male |
Ho |
|
|
Female |
Ho |
|
| Mean |
52 |
45 |
|
Mean |
38 |
45 |
|
| Variance |
316 |
0 |
|
Variance |
334.667 |
0 |
|
| Observations |
25 |
25 |
|
Observations |
25 |
25 |
|
| Hypothesized Mean Difference |
0 |
|
|
Hypothesized Mean Difference |
0 |
|
|
| df |
24 |
|
|
df |
24 |
|
|
| t Stat |
1.96890383 |
|
|
t Stat |
-1.9132 |
|
|
| P(T<=t) one-tail |
0.03030785 |
|
|
P(T<=t) one-tail |
0.03386 |
|
|
| t Critical one-tail |
1.71088208 |
|
|
t Critical one-tail |
1.71088 |
|
|
| P(T<=t) two-tail |
0.0606157 |
|
|
P(T<=t) two-tail |
0.06772 |
|
|
| t Critical two-tail |
2.06389856 |
|
|
t Critical two-tail |
2.0639 |
|
|
| Conclusion: Do not reject Ho; mean equals 45 |
Conclusion: Do not reject Ho; mean equals 45 |
| Is this a 1 or 2 tail test? |
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Is this a 1 or 2 tail test? |
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| - why? |
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- why? |
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| P-value is: |
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P-value is: |
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| Is P-value > 0.05? |
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Is P-value > 0.05? |
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| Why do we not reject Ho? |
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Why do we not reject Ho? |
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Question 2: Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other.
(Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.)
Ho:
Ha:
Test to use:
Place B43 in Outcome range box.
b. Since the one and two sample t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why?
Question 3: Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)
Ho:
Ha:
Statistical test to use:
Place B75 in Outcome range box.
Question 4: Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders?
Ho:
Ha:
Test to use:
Place B106 in Outcome range box.
Question 5: If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality,
which would be more appropriate to use in answering the question about salary equity? Why?
What are your conclusions about equal pay at this point?