Week 2Testing means
In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing.
In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis.
1Below 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 -- see column S)
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?
MalesFemales
Ho: Mean salary = 45Ho: Mean salary = 45
Ha: Mean salary =/= 45Ha: 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.
MaleHoFemaleHo
Mean5245Mean3845
Variance3160Variance334.66666670
Observations2525Observations2525
Hypothesized Mean Difference0Hypothesized Mean Difference0
df24df24
t Stat1.968903827t Stat-1.913206357
P(T<=t) one-tail0.03030785P(T<=t) one-tail0.033862118
t Critical one-tail1.71088208t Critical one-tail1.71088208
P(T<=t) two-tail0.060615701P(T<=t) two-tail0.067724237
t Critical two-tail2.063898562t Critical two-tail2.063898562
Conclusion: Do not reject Ho; mean equals 45Conclusion: Do not reject Ho; mean equals 45
Is this a 1 or 2 tail test?Is this a 1 or 2 tail test?
- why?- why?
P-value is:P-value is:
Is P-value > 0.05?Is P-value > 0.05?
Why do we not reject Ho?Why do we not reject Ho?
Interpretation:
2Based 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.
P-value is:
Is P-value < 0.05?
Reject or do not reject Ho:
If the null hypothesis was rejected, what is the effect size value:
Meaning of effect size measure: Interpretation:
b.Since the one and two tail t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why?
3Based 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.
What is the p-value:
Is P-value < 0.05?
Reject or do not reject Ho:
If the null hypothesis was rejected, what is the effect size value:
Meaning of effect size measure:
Interpretation:
4Since 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.
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If the null hypothesis was rejected, what is the effect size value:
Meaning of effect size measure:
Interpretation:
5If 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?