### Side effects for each brand of pain medication

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Part I. Chi-Square Goodness of Fit Test (equal frequencies)

Four different brands of a pain medication used for chronic back ailments were tested to see if the number of side effects for each brand were the same. The table below lists the results of the reported number of side effects for each brand of pain medication.

Brand A
Brand B
Brand C
Brand D
23
17
33
11

[Hint: Be sure to watch the video at Week 5 Resources on the "Chi-Square Goodness-of-Fit test (equal frequencies)" before attempting this problem. Instructions for performing this test in STATDISK can be found in the Statdisk User Manual.]

Instructions
1. Use the Chi-Square Goodness-of-Fit test to see if there is a difference between the number of side effects from the different brands of medication. Use a significance level of .01.
Paste results here.

2. What are we trying to show here?

3. What is the p-value and what does it represent in the context of this problem?

4. State in your own words what the results of this Goodness-of-fit test tells us.

5. Repeat the above procedure using only Brands A, B, and D. Paste results here.

6. Do you get a different result?

Part II. Chi-Square Goodness of Fit Test (unequal frequencies)

An opinion poll was taken to see how people felt about Health Care reform. Previous poll results indicate that within a particular population 34% were for reform, 41% were against reform, and 25% were uncertain.

This year, the following results were observed:

FOR: 317 people AGAINST: 223 people UNCERTAIN: 211 people

[Hint: Be sure to watch the video at Week 5 Resources on the "Chi-Square Goodness-of-Fit test (unequal frequencies)" before attempting this problem. Instructions for performing this test in STATDISK can be found in the Statdisk User Manual.]

Instructions
7. Complete the table as necessary.

[Hint: You will need to compute the expected frequencies based on the previous poll results. Round to the nearest integer.]

OBSERVED

EXPECTED

8. Use the Chi-Square Goodness-of-Fit test for Unequal frequencies to see if there is a difference between the observed frequencies (this year) and the expected frequencies (based on the previous poll results). Use a significance level of .01.
Paste results here.

9. State the null and alternative hypothesis.

10. What conclusion would you reach, given the result of your Goodness-of-Fit test? [State in your own words.]

Part III. Chi-Square Test of Independence

A study was done to test the claim that discharging a newborn infant discharged early (less than 30 hours after birth) is related to re-hospitalization of that infant within a week of discharge.

The following data was collected related to early discharge and re-hospitalization:

Re-hospitalized within 1 week
Not
re-hospitalized
Total
Early Discharge (less than 30 hours)
622
3997
4619
Late Discharge (30 - 78 hours)
631
4660
5291

Hint: Instructions for performing this test in STATDISK can be found in the Stat Disk User's Manual under the heading Chi Square Test of Independence (Contingency Tables).

Instructions

11. Just looking at the numbers in the table, what is your best guess about whether early discharge is related to re-hospitalization? [Hint: you might compute the difference in percentages between those that were discharged early and those that were not.]

12. Compute a Chi-Square Test of Independence on this data using a 0.05 level of significance. Paste your results here.

13. What is the null and alternative hypothesis for this result?

14. What is the p-value for this result? What does this represent?

15. State your conclusion related to the context of this problem.

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