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In a large clinical trial, 390,256 children were randomly assigned to two groups. The treatment group consisted of 193,731 children given a vaccine for a certain disease, and 32 of those children developed the disease. The other 196,525 children were given a placebo, and 127 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 0.01 significance level will be used to test the claim that p,

In a large clinical trial, 390,256 children were randomly assigned to two groups. The treatment group consisted of 193,731 children given a vaccine for a certain disease, and 32 of those children developed the disease. The other 196,525 children were given a placebo, and 127 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 0.01 significance level will be used to test the claim that p,

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 5E: List the sample space of each experiment. Rolling one die and tossing one coin
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In a large clinical trial, 390,256 children were randomly assigned to two groups. The treatment group consisted of 193,731 children given a vaccine for a certain disease, and 32 of those children developed the disease. The other 196,525 children were given a placebo, and 127 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 0.01 significance level will be used to test the claim that p, <p2. Which is better: A hypothesis test or a confidence interval? A hypothesis test 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; critical value method? P-value method and critical value method are equivalent, in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on the assumption that the two population proportions are equal, whereas the other method uses a standard deviation based on estimated values of the population proportions. c. If a 0.01 significance level is to be used to test the claim that p, <p2, what confidence level should be used? 98 % (Type an integer or a decimal.) d. If the claim in part (c) is tested using this sample data, we get this confidence interval: - 0.000631 <p, - p2 < - 0.000331. What does this confidence interval suggest about the claim? Because the confidence interval there a significant difference between the two proportions. Because the confidence interval consists it appears that the first proportion is the second proportion. There is 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.
Transcribed Image Text:In a large clinical trial, 390,256 children were randomly assigned to two groups. The treatment group consisted of 193,731 children given a vaccine for a certain disease, and 32 of those children developed the disease. The other 196,525 children were given a placebo, and 127 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 0.01 significance level will be used to test the claim that p, <p2. Which is better: A hypothesis test or a confidence interval? A hypothesis test 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; critical value method? P-value method and critical value method are equivalent, in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on the assumption that the two population proportions are equal, whereas the other method uses a standard deviation based on estimated values of the population proportions. c. If a 0.01 significance level is to be used to test the claim that p, <p2, what confidence level should be used? 98 % (Type an integer or a decimal.) d. If the claim in part (c) is tested using this sample data, we get this confidence interval: - 0.000631 <p, - p2 < - 0.000331. What does this confidence interval suggest about the claim? Because the confidence interval there a significant difference between the two proportions. Because the confidence interval consists it appears that the first proportion is the second proportion. There is 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.
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