BUS 308
jerain 1bus308_week_2_assignment.xlsx
question
Week 2 | Testing means with the t-test | <Note: use right click on row numbers to insert rows to perform analysis below any question> | |||||
For questions 2 and 3 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. | |||||||
For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed. | |||||||
1 | Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. | ||||||
Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female salaries? | |||||||
Males | Females | ||||||
Ho: Mean salary = 45 | Ho: Mean salary = 45 | ||||||
Ha: Mean salary =/= 45 | Ha: Mean salary =/= 45 | ||||||
Note when performing a one sample test with ANOVA, the second variable (Ho) is listed as the same value for every corresponding value in the data set. | |||||||
t-Test: Two-Sample Assuming Unequal Variances | t-Test: Two-Sample Assuming Unequal Variances | ||||||
Since the Ho variable has Var = 0, variances are unequal; this test defaults to 1 sample t in this situation | |||||||
Male | Ho | Female | Ho | ||||
Mean | 52 | 45 | Mean | 38 | 45 | ||
Variance | 316 | 0 | Variance | 334.6666666667 | 0 | ||
Observations | 25 | 25 | Observations | 25 | 25 | ||
Hypothesized Mean Difference | 0 | Hypothesized Mean Difference | 0 | ||||
df | 24 | df | 24 | ||||
t Stat | 1.9689038266 | t Stat | -1.9132063573 | ||||
P(T<=t) one-tail | 0.0303078503 | P(T<=t) one-tail | 0.0338621184 | ||||
t Critical one-tail | 1.7108820799 | t Critical one-tail | 1.7108820799 | ||||
P(T<=t) two-tail | 0.0606157006 | P(T<=t) two-tail | 0.0677242369 | ||||
t Critical two-tail | 2.0638985616 | t Critical two-tail | 2.0638985616 | ||||
Conclusion: Do not reject Ho; mean equals 45 | Conclusion: Do not reject Ho; mean equals 45 | ||||||
Interpretation: | |||||||
2 | Based on our sample results, perform a 2-sample t-test to see if the population male and female salaries could be equal to each other. | ||||||
3 | Based on our sample results, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.) | ||||||
4 | What other information would you like to know to answer the question about salary equity between the genders? Why? | ||||||
5 | If the salary and compa mean tests in questions 3 and 4 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? | |||||||
answer 1
1) | Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female salaries? |
Males | |
because the p-value = 0.061 is greater than alpha = 0.05, it implies that there is insufficient | |
evidence to indicate that the average salaries of males at this company is significantly | |
different than the company average for all employees. | |
Females | |
because the p-value = 0.068 is greater than alpha = 0.05, it implies that there is insufficient | |
evidence to indicate that the average salaries of females at this company is significantly | |
different than the company average for all employees. |
answer 2
2) | Based on our sample results, perform a 2-sample t-test to see if the population male and female salaries could be equal to each other. | ||||||
when the sample sizes are the same (as they are here), they are identical, i.e. both t-tests result in the same test statistic, the same p-value and the same conclusion. | |||||||
t-Test : Two-sample Assuming equal variances | t-Test : Two-sample Assuming Unequal variances | ||||||
Male-salay | Female-salary | Male-salay | Female-salary | ||||
mean | 52 | 38 | mean | 52 | 38 | ||
Variance | 316 | 334.6667 | Variance | 316 | 334.6667 | ||
Observations | 25 | 25 | Observations | 25 | 25 | ||
Pooled Variance | 325.3333 | Hypothesized mean Difference | 0 | ||||
Hypothesized mean Difference | 0 | degree of freedom | 48 | ||||
degree of freedom | 48 | t-stat | 2.744219 | ||||
t-Stat | 2.744219 | P(T ≤ t) one-tail | 0.004253 | ||||
P(T ≤ t) one-tail | 0.004253 | t Critical one-tail | 1.67724 | ||||
t Critical one-tail | 1.677224 | P(T ≤ t) Two-tail | 0.008506 | ||||
P(T ≤ t) Two-tail | 0.008506 | t Critical two-tail | 2.010635 | ||||
t Critical two-tail | 2.010635 | ||||||
Since the p-value = 0.008 is less than alpha = 0.05, it implies that there is sufficient evidence | |||||||
to indicate that the population average salaries of males and females at this company do significantly differ. |
answer3
3) | Based on our sample results, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.) | ||||||
t-Test: Two-Sample Assuming Equal Variances | t-Test: Two-Sample Assuming UnEqual Variances | ||||||
Male-compa | Female-compa | Male-compa | Female-compa | ||||
Mean | 1.05624 | 1.06872 | Mean | 1.05624 | 1.06872 | ||
Variance | 0.007021 | 0.004948 | Variance | 0.007021 | 0.004948 | ||
Observations | 25 | 25 | Observations | 25 | 25 | ||
Pooled Variance | 0.005984 | Hypothesized mean Difference | 0 | ||||
Hypothesized mean Difference | 0 | degree of freedom | 48 | ||||
degree of freedom | 48 | t-Stat | -0.57037 | ||||
t-Stat | -0.57037 | P(T ≤ t) one-tail | 0.285572 | ||||
P(T ≤ t) one-tail | 0.285544 | t Critical one-tail | 1.677927 | ||||
t Critical one-tail | 1.677224 | P(T ≤ t) Two-tail | 0.571144 | ||||
P(T ≤ t) Two-tail | 0.571088 | t Critical two-tail | 2.011741 | ||||
t Critical two-tail | 2.010635 | ||||||
Since the p-value = 0.571 is greater than alpha = 0.05, it implies that there is insufficient evidence to indicate that the average compa's of males | |||||||
and females at this company do significantly differ. This implies that the male and female compas in the population be equal to each other. |
answer4
4) | What other information would you like to know to answer the question about salary equity between the genders? Why? |
To test for salary equity, we should consider (factor in) the other variables that affect salary, e.g. years of service, the persons degree, the person's appraisal rating, etc. |
answer5
5) | If the salary and compa mean tests in questions 3 and 4 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? | |
Do the conclusions differ? Yes, the two t-test do offer different conclusions. | |
Why? The Compa variable remove the impact of grade. | |
My conclusion... Of the two t-tests, the better one is the on in which we compare compa's. Again, comparing compa's allows us to remove the impact of grade. |