Question

It has been observed that some persons who suffer colitis, again suffer colitis within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode? Select the [Alternative Hypothesis, Value of the Test Statistic].

Answer 1

Solution:

Null Hypothesis (Ho): p1 = p2

Alternative Hypothesis (Ha): p1= p2

Since sample size is large, we use Z-test.

Test Statistics

Z = (0.11 - 0.09)/(0.11)(1-0.11)/55 + (0.09)(1-0.09)/45

Z = 0.333

Using Z-tables, the critical value at a/2 = 0.1/2 = 0.05 is 1.645

Since test statistics lie within the critical values, we fail to reject Ho.

Hence, we cannot conclude that the true percentage of those in the first group who suffer a second episode is different from the true

percentage of those in the second group who suffer a second episode.