Score:
Week 2
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Testing means – T-tests
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.
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(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?
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
Mean
52
Variance
316
Observations
25
Hypothesized Mean D
0
df
24
t Stat
1.968903827
P(T<=t) one-tail
0.03030785
t Critical one-tail
1.71088208
P(T<=t) two-tail
0.060615701
t Critical two-tail
2.063898562
Ho
45
0
25
Conclusion: Do not reject Ho; mean equals 45
Is this a 1 or 2 tail test?
– why?
P-value is:
Is P-value > 0.05?
Why do we not reject Ho?
Interpretation:
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2
Female
Mean
38
Variance
334.667
Observations
25
Hypothesized Mean
0
df
24
t Stat
-1.91321
P(T<=t) one-tail
0.03386
t Critical one-tail
1.71088
P(T<=t) two-tail
0.06772
t Critical two-tail
2.0639
Ho
45
0
25
Conclusion: Do not reject Ho; mean equals 45
Is this a 1 or 2 tail test?
– why?
P-value is:
Is P-value > 0.05?
Why do we not reject Ho?
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.
P-value is:
Is P-value < 0.05?
Reject or do not reject Ho:
If the null hypothesis was rejected,
what of effect size measure:
Meaning is the effect size value:
Interpretation:
b. Since the one and two sample t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why?
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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:
Q3
Ho
Female
Male
Female
45
45
45
45
45
45
45
45
45
45
45
34
41
23
22
23
42
24
24
69
36
34
1.017
0.870
1.157
0.979
1.134
1.149
1.052
1.175
1.043
1.134
1.043
1.096
1.025
1.000
0.956
1.000
1.050
1.043
1.043
1.210
1.161
1.096
45
45
45
45
45
45
45
45
45
45
45
57
23
50
24
75
24
24
23
22
35
24
1.000
1.074
1.020
0.903
1.122
0.903
0.982
1.086
1.075
1.052
1.140
1.187
1.000
1.041
1.043
1.119
1.043
1.043
1.000
0.956
1.129
1.043
45
77
1.087
1.149
45
45
55
65
1.052
1.157
1.145
1.140
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 of effect size measure:
Meaning is the effect size value:
Interpretation:
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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.
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If the null hypothesis was
rejected,of effect the effect size
Meaning what is size measure:
value:
Interpretation:
<2 points> 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?
