# Bus 308 week 2 assignment

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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