| Score: | Week 2 | Testing means - T-tests | Q3 |
| In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. | Ho | Female | Male | Female |
| In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis. | 45 | 34 | 1.017 | 1.096 |
| 45 | 41 | 0.870 | 1.025 |
| <1 point> | 1 | Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. | 45 | 23 | 1.157 | 1.000 |
| (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) | 45 | 22 | 0.979 | 0.956 |
| 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? | 45 | 23 | 1.134 | 1.000 |
| Males | Females | 45 | 42 | 1.149 | 1.050 |
| Ho: Mean salary = 45 | Ho: Mean salary = 45 | 45 | 24 | 1.052 | 1.043 |
| Ha: Mean salary =/= 45 | Ha: Mean salary =/= 45 | 45 | 24 | 1.175 | 1.043 |
| 45 | 69 | 1.043 | 1.210 |
| Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, | 45 | 36 | 1.134 | 1.161 |
| 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. | 45 | 34 | 1.043 | 1.096 |
| Male | Ho | Female | Ho | 45 | 57 | 1.000 | 1.187 |
| Mean | 52 | 45 | Mean | 38 | 45 | 45 | 23 | 1.074 | 1.000 |
| Variance | 316 | 0 | Variance | 334.6666666667 | 0 | 45 | 50 | 1.020 | 1.041 |
| Observations | 25 | 25 | Observations | 25 | 25 | 45 | 24 | 0.903 | 1.043 |
| Hypothesized Mean Difference | 0 | Hypothesized Mean Difference | 0 | 45 | 75 | 1.122 | 1.119 |
| df | 24 | df | 24 | 45 | 24 | 0.903 | 1.043 |
| t Stat | 1.9689038266 | t Stat | -1.9132063573 | 45 | 24 | 0.982 | 1.043 |
| P(T<=t) one-tail | 0.0303078503 | P(T<=t) one-tail | 0.0338621184 | 45 | 23 | 1.086 | 1.000 |
| t Critical one-tail | 1.7108820799 | t Critical one-tail | 1.7108820799 | 45 | 22 | 1.075 | 0.956 |
| P(T<=t) two-tail | 0.0606157006 | P(T<=t) two-tail | 0.0677242369 | 45 | 35 | 1.052 | 1.129 |
| t Critical two-tail | 2.0638985616 | t Critical two-tail | 2.0638985616 | 45 | 24 | 1.140 | 1.043 |
| Conclusion: Do not reject Ho; mean equals 45 | Conclusion: Do not reject Ho; mean equals 45 | 45 | 77 | 1.087 | 1.149 |
| Is this a 1 or 2 tail test? | Is this a 1 or 2 tail test? |
| - why? | - why? |
| P-value is: | P-value is: | 45 | 55 | 1.052 | 1.145 |
| Is P-value > 0.05? | Is P-value > 0.05? | 45 | 65 | 1.157 | 1.140 |
| 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? |
MathematicsExpert
week_2_questions.xlsx
