Question

1) 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 55 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, 10% 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 0.01, 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].

a) [p1 = p2 , 0.1928] b) [p1 ≠ p2 , 0.1928] c) [p1 ≠ p2 , 0.2928] d) [p1 < p2 , 0.1928] e) [p1 > p2 , 0.1928] f) None of the above

2) 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 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 [Rejection Region, Decision to Reject (RH₀) or Failure to Reject (FRH₀)].

a) [z < -1.65, RH₀]

b) [z < -1.65 and z > 1.65, FRH₀]

c) [z > 1.65, FRH₀]

d) [z < -1.65 or z > 1.65, FRH₀]

e) [z > -1.65 and z < 1.65, RH₀]

f) None of the above

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

p1cap = X1/N1 = 5.5/55 = 0.1
p1cap = X2/N2 = 6.75/75 = 0.09
pcap = (X1 + X2)/(N1 + N2) = (5.5+6.75)/(55+75) = 0.0942

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.1-0.09)/sqrt(0.0942*(1-0.0942)*(1/55 + 1/75))
z = 0.1928

b) [p1 ≠ p2 , 0.1928]

2)

This is two tailed test, for α = 0.1
Critical value of z are -1.645 and 1.645.
Hence reject H0 if z < -1.645 or z > 1.645

d) [z < -1.65 or z > 1.65, FRH0]