BUS 308 Statistics for Managers Week 2 Assignment 2
| 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 | 334.667 | 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 | 1.96890383 | t Stat | -1.9132 | 45 | 24 | 0.982 | 1.043 | ||||||||||||||||||||||||||||
| P(T<=t) one-tail | 0.03030785 | P(T<=t) one-tail | 0.03386 | 45 | 23 | 1.086 | 1.000 | ||||||||||||||||||||||||||||
| t Critical one-tail | 1.71088208 | t Critical one-tail | 1.71088 | 45 | 22 | 1.075 | 0.956 | ||||||||||||||||||||||||||||
| P(T<=t) two-tail | 0.0606157 | P(T<=t) two-tail | 0.06772 | 45 | 35 | 1.052 | 1.129 | ||||||||||||||||||||||||||||
| t Critical two-tail | 2.06389856 | t Critical two-tail | 2.0639 | 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. | |||||||||||||||||||||||||||||||||
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