Question

Question 7 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 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? Select the [Alternative Hypothesis, Value of the Test Statistic). a) OPI <p2,-0.3129) b) Olpi > P2,-0.3129) c) OPP2.-0.2129] d) OPP2,-0.3129] e) OPI - 22.-0.3129) 1 None of the above

Answer 1

U het p represent the troue percentage of those in the ist group and Pa represents the true percentage of the second group We want to know if Pi <pa. :: Null hypothesis Ho: P2P2 Alternate hypothes's Hai P,<P2 P = proportion of the st group = 12-0112 8 = proportion of the and group = 14 = 0.14 Test statistic zz - SE where se Jør CI-D) * C * 72 where n, = sample size of the ist group = 45 na = Sample size of the and group = 15 6 - pooled pooportion = Ô * 0,+ Pa* na .0.12*45+0.14*75 45 + 75 notna 5.4+10.5, 0.1325 120 .: SE: J0-132540-86754 [+ + +] 0.1325 +0.8675*6.0222 +0.0133) 10.004080 = 0.06387 -0.02 -0.02 0.06 387 -0.3129 .. 012-0:14 0.06387 3129 0.0639 so Answer is ophion A- [..<P2 ,-0. 3129]. p (value) = PC 3<-0.3129) = Area of the shaded Begion under Standard noomal curve -0.31710

= 0.3772 As p-value (0.3772) is greater than the significarea level (0:1) lake can't reject Ho. So we accepi Ho and Teject the hull hypothesis that P, <Po . So we conclude that there is no sufficient evidence to believe that the true percentage of those in the first group who suffer a recond episode is significantly less than the true percentage of those in the second group who suffer a second episode.