Question

It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn 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 45 people in the first group and this group will be administered the new drug. There are 75 people in the second group and this group will be administered a placebo. After one year, 12% of the first group has a second episode and 14% 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 less than the true percentage of those in the second group who suffer a second episode.

A. [ z < -1.65, RHo].
B. [ z < -1.65 and z > 1.65, FRHo].
C. [z > 1.65, FRHo].
D. [z < -1.65 and z > 1.65, FRHo].
E. [z > -1.65 and z < 1.65, RHo].
F. None of the above.

Answer 1

F. None of the above.

Explanation:

Let the null and alternate hypothesis be

H0: p1 ≥ p2 against the claim Ha: p1 < p2

the significance level is 0.1

The critical region is z < z∝= 1.28

The test statistic is

Z= ( p^1-p^2)- (p1-p2)/√p1^q1^/n1 + p2^q2^/n2

Here n1= 45 , n2= 75

p1= 0.12 p2= 0.14

q1= 0.88 q2= 0.86

z= 0.12- 0.14/√0.12*0.88/45 +0.14*0.86/75

Z= 0.02/ √0.00235 + 0.00161

Z= 0.02/0.062891

z= 0.318

The calculated value of z= 0.318 lies in the critical region z < 1.28

therefore accept Ha.

All of the options are incorrect as the critical value for one tailed test for 0.1 is 1.28 .