Week 2

Testing means

 

 

 

 

 

 

 

 

 

 

 

 

 

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:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 tail 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:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 BUS 308 Week 2

Week 2

Testing means

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:

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 tail 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?

 

 

 

 

 

 

 

 

 

 

 

 

 

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?