BUS308 Week 2 Employee Salary Data (New Questions)
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Week 2 | Testing 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. | ||||||||||||||
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 tail 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 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: | ||||||||||||||
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: | ||||||||||||||
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? | ||||||||||||||
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