Score: |
Week 4 |
Confidence Intervals and Chi Square (Chs 11 – 12) |
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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. |
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For full credit, you need to also show the statistical outcomes – either the Excel test result or the calculations you performed. |
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<1 point> |
1 |
Using our sample data, construct a 95% confidence interval for the population’s mean salary for each gender. |
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Interpret the results. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)? |
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Mean |
St error |
t value |
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Low |
to |
High |
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Males |
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Females |
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<Reminder: standard error is the sample standard deviation divided by the square root of the sample size.> |
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Interpretation: |
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<1 point> |
2 |
Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population. |
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How does this compare to the findings in week 2, question 2? |
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Difference |
St Err. |
T value |
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Low |
to |
High |
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Yes/No |
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Can the means be equal? |
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Why? |
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How does this compare to the week 2, question 2 result (2 sampe t-test)? |
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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? |
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<1 point> |
3 |
We found last week that the degree values within the population do not impact compa rates. |
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This does not mean that degrees are distributed evenly across the grades and genders. |
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Do males and females have athe same distribution of degrees by grade? |
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(Note: while technically the sample size might not be large enough to perform this test, ignore this limitation for this exercise.) |
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What are the hypothesis statements: |
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Ho: |
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Ha: |
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Note: You can either use the Excel Chi-related functions or do the calculations manually. |
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Data input tables – graduate degrees by gender and grade level |
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OBSERVED |
A |
B |
C |
D |
E |
F |
Total |
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If desired, you can do manual calculations per cell here. |
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M Grad |
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A |
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D |
E |
F |
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Fem Grad |
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M Grad |
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Male Und |
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Fem Grad |
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Female Und |
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Male Und |
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Female Und |
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Sum = |
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EXPECTED |
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M Grad |
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For this exercise – ignore the requirement for a correction factor |
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Fem Grad |
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for cells with expected values less than 5. |
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Male Und |
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Female Und |
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Interpretation: |
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What is the value of the chi square statistic: |
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What is the p-value associated with this value: |
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Is the p-value <0.05? |
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Do you reject or not reject the null hypothesis: |
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If you rejected the null, what is the Cramer’s V correlation: |
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What does this correlation mean? |
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What does this decision mean for our equal pay question: |
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<1 point> |
4 |
Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern |
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within the population? |
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What are the hypothesis statements: |
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Ho: |
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Ha: |
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Do manual calculations per cell here (if desired) |
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A |
B |
C |
D |
E |
F |
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A |
B |
C |
D |
E |
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OBS COUNT – m |
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M |
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OBS COUNT – f |
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F |
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Sum = |
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EXPECTED |
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What is the value of the chi square statistic: |
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What is the p-value associated with this value: |
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Is the p-value <0.05? |
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Do you reject or not reject the null hypothesis: |
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If you rejected the null, what is the Phi correlation: |
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What does this correlation mean? |
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What does this decision mean for our equal pay question: |
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<2 points> |
5. How do you interpret these results in light of our question about equal pay for equal work? |
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