In a large clinical trial, 399,342 children were randomly assigned to two groups. The treatment group consisted of 201,406 children given a vaccine for a certain disease, and 27 of those children developed the disease. The othe children were given a placebo, and 93 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,

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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In a large clinical trial, 399,342 children were randomly assigned to two groups. The treatment group consisted of 201,406 children given a vaccine for a certain disease, and 27 of those children developed the disease. The other 197,936 children were given a placebo, and 93 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts (a) through (c) below.

**a.** Assume that a 0.01 significance level will be used to test the claim that \( p_1 < p_2 \). 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 \( p_1 < p_2 \), what confidence level should be used?

- **99%** (Type an integer or a decimal.)
Transcribed Image Text:### Transcript for Educational Website In a large clinical trial, 399,342 children were randomly assigned to two groups. The treatment group consisted of 201,406 children given a vaccine for a certain disease, and 27 of those children developed the disease. The other 197,936 children were given a placebo, and 93 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts (a) through (c) below. **a.** Assume that a 0.01 significance level will be used to test the claim that \( p_1 < p_2 \). 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 \( p_1 < p_2 \), what confidence level should be used? - **99%** (Type an integer or a decimal.)
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