+1 862 207 3288 Business 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.
<1 point> 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 — 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 Ho Female Ho
Mean 52 45 Mean 38 45
Variance 316 0 Variance 334.6666667 0
Observations 25 25 Observations 25 25
Hypothesized Mean Difference 0 Hypothesized Mean Difference 0
df 24 df 24
t Stat 1.968903827 t Stat -1.913206357
P(T<=t) one-tail 0.03030785 P(T<=t) one-tail 0.033862118
t Critical one-tail 1.71088208 t Critical one-tail 1.71088208
P(T<=t) two-tail 0.060615701 P(T<=t) two-tail 0.067724237
t Critical two-tail 2.063898562 t Critical two-tail 2.063898562
Conclusion: Do not reject Ho; mean equals 45 Conclusion: 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:
<1 point> 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.
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 sample t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why?
<1 point> 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.
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:
<1 point> 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, what is the effect size value:
Meaning of effect size measure:
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?
See comments at the right of the data set.
ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Grade
8 23 1.000 23 32 90 9 1 5.8 0 F A
10 22 0.956 23 30 80 7 1 4.7 0 F A
11 23 1.000 23 41 100 19 1 4.8 0 F A
14 24 1.043 23 32 90 12 1 6 0 F A
15 24 1.043 23 32 80 8 1 4.9 0 F A
23 23 1.000 23 36 65 6 1 3.3 1 F A
26 24 1.043 23 22 95 2 1 6.2 1 F A
31 24 1.043 23 29 60 4 1 3.9 0 F A
35 24 1.043 23 23 90 4 1 5.3 1 F A
36 23 1.000 23 27 75 3 1 4.3 1 F A
37 22 0.956 23 22 95 2 1 6.2 1 F A
42 24 1.043 23 32 100 8 1 5.7 0 F A
3 34 1.096 31 30 75 5 1 3.6 0 F B
18 36 1.161 31 31 80 11 1 5.6 1 F B
20 34 1.096 31 44 70 16 1 4.8 1 F B
39 35 1.129 31 27 90 6 1 5.5 1 F B
7 41 1.025 40 32 100 8 1 5.7 0 F C
13 42 1.050 40 30 100 2 1 4.7 1 F C
22 57 1.187 48 48 65 6 1 3.8 0 F D
24 50 1.041 48 30 75 9 1 3.8 1 F D
45 55 1.145 48 36 95 8 1 5.2 0 F D
17 69 1.210 57 27 55 3 1 3 0 F E
48 65 1.140 57 34 90 11 1 5.3 1 F E
28 75 1.119 67 44 95 9 1 4.4 1 F F
43 77 1.149 67 42 95 20 1 5.5 1 F F
19 24 1.043 23 32 85 1 0 4.6 1 M A
25 24 1.043 23 41 70 4 0 4 0 M A
40 25 1.086 23 24 90 2 0 6.3 0 M A
2 27 0.870 31 52 80 7 0 3.9 0 M B
32 28 0.903 31 25 95 4 0 5.6 0 M B
34 28 0.903 31 26 80 2 0 4.9 1 M B
16 47 1.175 40 44 90 4 0 5.7 0 M C
27 40 1.000 40 35 80 7 0 3.9 1 M C
41 43 1.075 40 25 80 5 0 4.3 0 M C
5 47 0.979 48 36 90 16 0 5.7 1 M D
30 49 1.020 48 45 90 18 0 4.3 0 M D
1 58 1.017 57 34 85 8 0 5.7 0 M E
4 66 1.157 57 42 100 16 0 5.5 1 M E
12 60 1.052 57 52 95 22 0 4.5 0 M E
33 64 1.122 57 35 90 9 0 5.5 1 M E
38 56 0.982 57 45 95 11 0 4.5 0 M E
44 60 1.052 57 45 90 16 0 5.2 1 M E
46 65 1.140 57 39 75 20 0 3.9 1 M E
47 62 1.087 57 37 95 5 0 5.5 1 M E
49 60 1.052 57 41 95 21 0 6.6 0 M E
50 66 1.157 57 38 80 12 0 4.6 0 M E
6 76 1.134 67 36 70 12 0 4.5 1 M F
9 77 1.149 67 49 100 10 0 4 1 M F
21 76 1.134 67 43 95 13 0 6.3 1 M F
29 72 1.074 67 52 95 5 0 5.4 0 M F
