. 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 skinrelated 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 skinrelated 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.
 How many variables were recorded in this study?
 Of those with nofamily history of skinissues, what proportion
did not present any symptoms of itching and what proportion
displayed symptoms of extreme itching?
 Of those witha family history of skinissues, what proportion
did not present any symptoms of itching and what proportion
displayed symptoms of extreme itching?
 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?
 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

 Comment on the appropriateness of the chisquare test for these
data. Are all necessary assumptions and conditions
verified? Explain briefly.
 Calculate the statistic. Show all supporting
work.
 How many degrees of freedom would you use to calculate this
pvalue in this example?