Question

.  The following data are from a dermatological study on  = 358 patients.  Several variables were recorded about the health of a patient’s skin, along with their family history of skin-related issues.  In the table provided, we have counts listed for two separate categorical variables:

Observed		Itching Status
		0	1	2	3	Row Total
Family History	0	97	58	91	68
	1	19	14	6	5
Column Total						358

• Family History(0 – no family history, 1 – family history of skin-related disease)
• Itching Status(0 – not present, 1 – little to no itching, 2 – moderate itching, 3 – extreme itching)

Use the information provided to answer the following questions.

1. How many variables were recorded in this study?

2. Of those with nofamily history of skin-issues, what proportion did not present any symptoms of itching and what proportion displayed symptoms of extreme itching?

3. Of those witha family history of skin-issues, what proportion did not present any symptoms of itching and what proportion displayed symptoms of extreme itching?

4. We wish to test to see if there is an association between these two variables.  What are the null and alternative hypotheses for this test?

5. For each cell, calculate the expected counts under the null hypothesis.  You may find it helpful to write the row and column totals first.

Expected		Itching Status
		0	1	2	3	Row Total
Family History	0
	1
Column Total						358

6. Comment on the appropriateness of the chi-square test for these data.  Are all necessary assumptions and conditions verified? Explain briefly.

7. Calculate the -statistic.  Show all supporting work.

8. How many degrees of freedom would you use to calculate this p-value in this example?  

Answer 1