Solutions to Selected Exercises 185smoked at least 250 cigarettes in their lifetime. Suppose Table 8.14 represents
the outcome of the survey.
Determine if there is a relationship between cigarette usage and reported
health status at the 5% signifi cance level one - sided. What is the p - value for the
chi - square test? Why is it appropriate to use the chi - square test?
Yes, we reject the null hypothesis at the 0.05 level. Based on SAS Version 9.2 Proc
Freq, chi - square p - value < 0.0001, indicating a highly signifi cant relationship
between smoking frequency and health status. Over 70% of the patients in the
excellent category smoke fewer than 250 cigarettes. Similarly, 58% of patients in
the good health category smoke fewer than 250 cigarettes. In the poor health cat-
egory, 53% are from the smoke fewer than 250 cigarettes. But in the very poor
health category 64% are from the smoke 250 or more category
The chi square test is appropriate because the sample sizes are large and each cat-
egory has at least 20 counts.- A clinical trial is conducted at an academic medical center. Diabetic patients
were randomly assigned to a new experimental drug to control blood sugar
levels versus a standard approved drug using a 1 : 1 randomization. 200 patients
were assigned to each group and the 2 × 2 table (Table 8.18 ) shows the results.
Test at the 5% level to determine if the new drug is more effective. Is it
appropriate to apply the chi - square test? Why would it be diffi cult to do
Fisher ’ s test without a computer? How many contingency tables are possible
with the given row and column marginal totals?
Based on both the chi - square test and Fisher ’ s exact test, we see that the drug is very
effective. p - value for both test is much less than 0.0001. The chi - square test s appropri-
ate because each cell has at least 21 patients in it. Fisher ’ s test would be diffi cult to do
by hand because there are many contingency tables to look at. But using SAS 9.2, this
is not really a problem. There are 141 such tables with the fi xed marginal totals.
Chapter 9- Apply the Wilcoxon rank - sum test to the data in the following table on the rela-
tionship between the number of patients with schizophrenia and the season of
their birth by calling fall and winter as group 1 and spring and summer as
group 2. The four individual seasons represent data points for each group.
Ignore the possibility of a year effect (Table 9.6 ).
Do we need to assume that births are uniformly distributed? If we knew
that there were a higher percentage of births in the winter months how would
that affect the conclusion?
The ordered data and ranks are as follows:
9 — summer 1
10 — spring 2
13 — spring 3
14 — spring 4
15 — summer 5bboth.indd 185oth.indd 185 6 6/15/2011 4:08:22 PM/ 15 / 2011 4 : 08 : 22 PM