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.]

Instructions
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.
Paste results here.

2. What are we trying to show here?
We are trying to check whether the side effects for all brands are same.
So, hypotheses to test the above objective are set as follows:
Null: The number of side effects of pain medicine are same for all four brands.

3. What is the p-value and what does it represent in the context of this problem?
From the output, the P-vlue = 0.0057
Since the P-value is less than the significance level, 0.01, reject the null hypotheses.

4. State in your own words what the results of this Goodness-of-fit test tells us.
Hence, it can be concluded that there is not sufficient evidence to support the claim that the number of side effects are not same for all medicines.

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

6. Do you get a different result?
Yes, the results in this case are completely different compared to previous conclusion.

In this case, the P-value is 0.1203 which is higher than the significance level. Therefore, do not reject the null hypothesis.
Hence, it can be concluded that there is sufficient evidence to support the claim that the number of side effects are same for all medicines