# STAT 3001 Week 5 Project: The Chi-Square Test

August 30, 2017

Question
Week 5 Project

STAT 3001

Week 5 Project: The Chi-Square Test

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 lists the results of the reported number of side effects for each brand of pain medication.

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Brand A

Brand B

Brand C

Brand D

23

17

13

11

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. Set the significance level to .01. Describe the

necessary Statdisk steps

Num Categories: 4

Degrees of freedom: 3

Expected Freq: 16

2) List the test statistics, p-value and whether to accept or reject the null hypothesis.

Test Statistic, X^2: 5.2500

Critical X^2: 11.34488

P-Value: 0.1544

3) State in your own words what the results of the hypothesis test is telling us.

Chi-Square Goodness-of-Fit Test (unequal frequencies)

An opinion poll was taken to see how people felt about Health Care reform. The table lists the number of responses for each option. Test to see if the poll results support previous data collection that showed 31% for, 44% against, and 25% uncertain.

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For

Against

Uncertain

Observed

217

223

211

Expected

4) Fill in the expected values (list counts only, not percentages) for the given table.

5) Use the Chi-Square Goodness-of-Fit test to see if there is a difference between observed and

expected values. Set the significance level to .10. Show the Statdisk output.

6) List whether to accept or reject the null hypothesis and why.

7) State in your own words what the results of the hypothesis test is telling us.

Week 5 Project

Chi-Square Test of Independence

Use the following observed values shown in the contingency table to test the independence between early discharge and re-hospitalization of newborns. Use a 0.05 level of significance to test the claim that whether a newborn was discharged early or late is related to whether the newborn was re-hospitalized within a week of discharge. Use the results of the Chi-Square Test of Independence to answer problem numbers 9 – 12.

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Yes

No

Early Discharge (less than 30 hours)

622

3997

Late Discharge (30 – 78 hours)

631

4660

Late Discharge ( > 78 hours)

316

2412

8) Run a Chi-Square Test of Independence. Show the Statdisk output.

9) Identify the test statistic. What does the number represent?

10) Identify the P?value. What does the number represent with respect to the study?

11) State your conclusion of the hypothesis test (reject or fail to reject)?