onfidence Intervals and Chi Square (Chs 11 – 12) | |||||||||||||||||||||||||||||||||

For questions 3 and 4 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 point> | 1 | Using our sample data, construct a 95% confidence interval for the population’s mean salary for each gender. | |||||||||||||||||||||||||||||||

Interpret the results. How do they compare with the findings in the week 2 one (Question 1)? | |||||||||||||||||||||||||||||||||

Mean | St error | t value | Low | to | High | ||||||||||||||||||||||||||||

Males | |||||||||||||||||||||||||||||||||

Females | |||||||||||||||||||||||||||||||||

<Reminder: standard error is the sample standard deviation divided by the square root of the sample size.> | |||||||||||||||||||||||||||||||||

Interpretation: | |||||||||||||||||||||||||||||||||

<1 point> | 2 | Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population. | |||||||||||||||||||||||||||||||

How does this compare to the findings in week 2, question 2? | |||||||||||||||||||||||||||||||||

Difference | St Err. | T value | Low | to | High | ||||||||||||||||||||||||||||

Yes/No | |||||||||||||||||||||||||||||||||

Can the means be equal? | Why? | ||||||||||||||||||||||||||||||||

How does this compare to the week 2, question 2 result (2 sampe t-test)? | |||||||||||||||||||||||||||||||||

a. | Why is using a two sample tool (t-test, confidence interval) a better choice than when comparing two samples? | ||||||||||||||||||||||||||||||||

<1 point> | 3 | We found last week that the degree values within the population do not impact compa rates. | |||||||||||||||||||||||||||||||

This does not mean that degrees are distributed evenly across the grades and genders. | |||||||||||||||||||||||||||||||||

Do males and females have athe same distribution of degrees by grade? | |||||||||||||||||||||||||||||||||

(Note: while technically the sample size might not be large enough to perform this test, ignore this limitation for this exercise.) | |||||||||||||||||||||||||||||||||

What are the hypothesis statements: | |||||||||||||||||||||||||||||||||

Ho: | |||||||||||||||||||||||||||||||||

Ha: | |||||||||||||||||||||||||||||||||

Note: You can either use the or do the calculations manually. | |||||||||||||||||||||||||||||||||

Data input tables – graduate degrees by gender and grade level | |||||||||||||||||||||||||||||||||

OBSERVED | A | B | C | D | E | F | Total | If desired, you can do manual calculations per cell here. | |||||||||||||||||||||||||

A | B | C | D | E | F | ||||||||||||||||||||||||||||

Fem Grad | M Grad | ||||||||||||||||||||||||||||||||

Male Und | Fem Grad | ||||||||||||||||||||||||||||||||

Female Und | Male Und | ||||||||||||||||||||||||||||||||

Female Und | |||||||||||||||||||||||||||||||||

Sum = | |||||||||||||||||||||||||||||||||

EXPECTED | |||||||||||||||||||||||||||||||||

M Grad | For this exercise – ignore the requirement for a correction factor | ||||||||||||||||||||||||||||||||

Fem Grad | for cells with expected values less than 5. | ||||||||||||||||||||||||||||||||

Male Und | |||||||||||||||||||||||||||||||||

Female Und | |||||||||||||||||||||||||||||||||

Interpretation: | |||||||||||||||||||||||||||||||||

What is the value of the chi square statistic: | |||||||||||||||||||||||||||||||||

What is the p-value associated with this value: | |||||||||||||||||||||||||||||||||

Is the p-value <0.05? | |||||||||||||||||||||||||||||||||

Do you reject or not reject the null hypothesis: | |||||||||||||||||||||||||||||||||

If you rejected the null, what is the Cramer’s V correlation: | |||||||||||||||||||||||||||||||||

What does this correlation mean? | |||||||||||||||||||||||||||||||||

What does this decision mean for our equal pay question: | |||||||||||||||||||||||||||||||||

<1 point> | 4 | Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern | |||||||||||||||||||||||||||||||

within the population? | |||||||||||||||||||||||||||||||||

What are the hypothesis statements: | |||||||||||||||||||||||||||||||||

Ho: | |||||||||||||||||||||||||||||||||

Ha: | |||||||||||||||||||||||||||||||||

Do manual calculations per cell here (if desired) | |||||||||||||||||||||||||||||||||

A | B | C | D | E | F | A | B | C | D | E | F | ||||||||||||||||||||||

OBS COUNT – m | M | ||||||||||||||||||||||||||||||||

OBS COUNT – f | F | ||||||||||||||||||||||||||||||||

Sum = | |||||||||||||||||||||||||||||||||

EXPECTED | |||||||||||||||||||||||||||||||||

What is the value of the chi square statistic: | |||||||||||||||||||||||||||||||||

What is the p-value associated with this value: | |||||||||||||||||||||||||||||||||

Is the p-value <0.05? | |||||||||||||||||||||||||||||||||

Do you reject or not reject the null hypothesis: | |||||||||||||||||||||||||||||||||

If you rejected the null, what is the Phi correlation: | |||||||||||||||||||||||||||||||||

What does this correlation mean? | |||||||||||||||||||||||||||||||||

What does this decision mean for our equal pay question: | |||||||||||||||||||||||||||||||||

<2 points> | 5. How do you interpret these results in light of our question about equal pay for equal work? | ||||||||||||||||||||||||||||||||

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