Week 2 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 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 334.667 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? 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: 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? 3 Based on our sample data set, can the male and female compas in the population be e.

1. Week 2
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.

2. 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

3. 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

4. Mean
38
45
Variance
316
0
Variance
334.667
0
Observations
25
25
Observations
25
25
Hypothesized Mean Difference
0
Hypothesized Mean Difference
0

5. 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

6. 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?
Is this a 1 or 2 tail test?

7. - why?
- why?
P-value is:
P-value is:
Is P-value > 0.05?
Is P-value > 0.05?
Why do we not reject Ho?

8. Why do we not reject Ho?
Interpretation:

9. 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.)

10. Ho:
Ha:
Test to use:
Place
B43 in Outcome range box.

15. P-value is:
Is P-value < 0.05?
Reject or do not reject Ho:

16. If
the null hypothesis was rejected, what is the effect size value:
Meaning of effect size measure:

17. 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?

18. 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:

19. Ha:
Statistical test to use:
Place
B75 in Outcome range box.

24. 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:

25. Meaning of effect size measure:
Interpretation:

26. 4
Since performance is often a factor in pay levels, is the average
Performance Rating the same for both genders?
Ho:
Ha:

27. Test to use:

28. Place
B106 in Outcome range box.

32. What is the p-value:

33. 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:

34. Interpretation:

35. 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?