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 helper video available 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.]
Answers:
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.
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 helper video available 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.]
Answers
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.
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: Be sure to watch the helper video available 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.]
Answers
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.
Part IV. Apply this to your own situation
Using one of the above statistical tests, compose and SOLVE an actual problem from the context of your own personal or professional life. You will need to make up some data and describe which test you will use to analyze the situation. Here's an example:
Example
State the problem that you are analyzing.
Last year, I asked the kids in my neighborhood what kind of cookies they preferred. 50% said chocolate-chip, 20% said oatmeal-raisin, and 30% said sugar cookie. I want to see if this has changed.
Make up some data for the new situation.
I asked 50 neighborhood kids what kind of cookie they preferred now and here's what they said:
· 35 said chocolate-chip
· 5 said oatmeal-raisin
· 10 said sugar-cookie
Determine which type of Chi-Square test you will perform.
Since these are unequal frequencies, I will perform a Chi-Square Goodness-of-Fit Test (Unequal Frequencies).
Specify your null and alternative hypotheses.
H0: There is no difference this year in the preferences of cookies within the neighborhood kids.
H1: Things have changed.
Setup the test
Chocolate-Chip
Oatmeal-Raisin
Sugar-Cookie
OBSERVED
35
5
10
EXPECTED
25
10
15
Perform the test