In randomized, double blind clinical trials of a neww vaccine monkeys were 114 o
ID: 3314060 • Letter: I
Question
In randomized, double blind clinical trials of a neww vaccine monkeys were 114 of 745 subjects in the experimental group (group 1) expedienced drowsiness as a side effect After the second dose, 49 of 563 of evidence sugest that a higher proporion ofsutiesingop le pedesced lever as a side old han stets n goup 2 ane-010 leddup kace randonly dvided into two groups Subjects in group 1 recelved the new vaccine white subjects in group 2 received a control vaccine Ater the second dose Veily the model requiremsents Select al that apply A. The sample size is less than 5% offepopuliden size for each sample B. nm(1-p ) 210and n2h(12)210 c. The data con" from a population that is norma,, Mbuted D. The samples are independent E. The sample size is merena, 5% ofthe population size for each sample F. The samples are dependent Determine the nal and altemative hypothese Ho P Fnd ted stlk fo.is hypothesis test Roand to two decial places as Cck to seect your answersExplanation / Answer
Solution:-
(B) n1p1(1 - p1) > 10 and n2p2(1 - p2) > 10
C) The samples are independent.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1< P2
Alternative hypothesis: P1 > P2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.1246
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.01844
z = (p1 - p2) / SE
z = 3.58
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 3.58. We use the Normal Distribution Calculator to find P(z > 3.58).
Thus, the P-value = less than 0.001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.10), we have to reject the null hypothesis.
(C) Reject H0, There is sufficient evidence to conclude that a higher proportion of subjects in group 1 experienced depression as sideeffects than the subjects in grouop 2 at the alpha = 0.10 level of significance.
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