# BUS308 – WEEK 4

Score: | Week 4 | Confidence 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 sample t-test outcomes (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 using 2 one-sample techniques 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 Excel Chi-related functions 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. | |||||||

M Grad | 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 | |||||

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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