Question

It has been observed that some persons who suffer renal failure, again suffer renal failure 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 31 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 more than the true percentage of those in the second group who suffer a second episode? select the [rejection region, decision to reject (rh0) or failure to reject (frh0)].

a [z < -1.28 or z > 1.28, rh0]
b [z < -1.28 and z > 1.28, frh0]
c [z > 1.28, frh0]
d [z > -1.28 and z < 1.28, rh0]
e [z < -1.28, frh0] f none of the above

Answer 1

The correct answer is [z < -1.28 or z > 1.28, rh0]. Hence the correct option is a.

We want to test if the new drug (first group) significantly reduces the chance of a second episode compared to the placebo (second group). This implies a one-tailed test where we reject the null hypothesis (H₀: drug has no effect) only if the proportion of second episodes in the first group is significantly lower than the second group.

The significance level is 0.1, meaning we reject the null hypothesis only if the p-value is less than 0.1.

Z-test is appropriate for testing the difference between two proportions when sample sizes are large enough.

Based on the information, we can calculate the test statistic (z) and compare it to the critical value for a one-tailed test at α = 0.1 (z ≈ -1.28).

Therefore, only option aligns with the one-tailed test and critical value for significance level 0.1, leading to rejection of the null hypothesis if z falls outside the specified rejection region. The other options either represent two-tailed tests, incorrect critical values, or incorrect rejection decisions. Hence the correct option is a.