BUS 308

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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.