Question

In a large clinical trial, 393,888 children were randomly assigned to two groups. The treatment group consisted of 198,120 children given a vaccine for a certain disease, and 38 of those children developed the disease. The other 195,768 children were given a placebo, and 116 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts (a) through (d) below. a. Assume that a 0.05 signiticance level will e used to test the claim that p1 P2.Which is better: A hypothesis test or a confidence interva? V is better b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; P-value method: ritical value method? ? are equivalent, in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on Vwhereas the other method uses a standard deviation based on c. If a 0.05 significance level is to be used to test the claim that p1 p2, what confidence level should be used? (Type an integer or a decimal.) d. If the claim in part (is tested using this sample data we get this confidence interval -0.000505<p1-p2 <-0.000297 What does this confidence interval suggest about the claim? there Va significant difference between the two proportions. Because the Because the confidence interval confidence interval consists proportion. There is Vit appears that the first proportion is ?| the second evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo

Answer 1

(a) A hypothesis test is better. P-value method and critical value method are equivalent Both of these methods use a standard deviation based on population Whereas the other method uses a standard deviation based on sample values The confidence level that should be used is 1-005-9590 (d) Because the interval -0.000505,-0.000297 does not contain zero there is a significant difference between the two proportions. Because the confidence interval consists of negative values it appears that the first proportion is smaller than the second. There is enough evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo