| 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 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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