In a large clinical trial, 394,521 children were randomly assigned to two groups. The treatment group consisted of 198,315 children given a vaccine for a certain diseas and 40 of those children developed the disease. The other 196,206 children were given a placebo, and 138 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 0.10 significance level will be used to test the claim that p,

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_In a large clinical trial, 394,521 children were randomly assigned to two groups. The treatment group consisted of 198,315 children given a vaccine for a certain disease, and 40 of those children developed the disease. The other 196,206 children were given a placebo, and 138 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 0.10 significance level will be used to test the claim that \( p_1 < p_2 \). Which is better: A hypothesis test or a confidence interval?_

\[ \boxed{\text{(Select one of the options)}} \] 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?_

\[ \boxed{\text{(Select two methods)}} \] are equivalent in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on \[ \boxed{\text{(Select one: Combined sample proportion, Weighted average)}} \] whereas the other method uses a standard deviation based on \[ \boxed{\text{(Select one: Combined sample proportion, Weighted average)}} \] 

_c. If a 0.10 significance level is to be used to test the claim that \( p_1 < p_2 \), what confidence level should be used?_

\[ \boxed{\text{(Type an integer or a decimal)}} \% \]

_d. If the claim in part (c) is tested using this sample data, we get this confidence interval - \( 0.000589 < p_1 - p_2 < -0.000415 \). What does this confidence interval suggest about the claim?_

Because the confidence interval \[ \boxed{\text{contains/does not contain}} \] zero, there \[ \boxed{\text{(is/is not)}} \] a significant difference between the two proportions. Because the confidence interval consists \[ \boxed{\text{(entirely of negative values/entirely of positive values)}} \], it appears that the first proportion is \[ \boxed{\text{(less than/greater than/equal to)}} \] the second proportion. There is \[ \boxed{\text{(sufficient/
Transcribed Image Text:_In a large clinical trial, 394,521 children were randomly assigned to two groups. The treatment group consisted of 198,315 children given a vaccine for a certain disease, and 40 of those children developed the disease. The other 196,206 children were given a placebo, and 138 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 0.10 significance level will be used to test the claim that \( p_1 < p_2 \). Which is better: A hypothesis test or a confidence interval?_ \[ \boxed{\text{(Select one of the options)}} \] 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?_ \[ \boxed{\text{(Select two methods)}} \] are equivalent in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on \[ \boxed{\text{(Select one: Combined sample proportion, Weighted average)}} \] whereas the other method uses a standard deviation based on \[ \boxed{\text{(Select one: Combined sample proportion, Weighted average)}} \] _c. If a 0.10 significance level is to be used to test the claim that \( p_1 < p_2 \), what confidence level should be used?_ \[ \boxed{\text{(Type an integer or a decimal)}} \% \] _d. If the claim in part (c) is tested using this sample data, we get this confidence interval - \( 0.000589 < p_1 - p_2 < -0.000415 \). What does this confidence interval suggest about the claim?_ Because the confidence interval \[ \boxed{\text{contains/does not contain}} \] zero, there \[ \boxed{\text{(is/is not)}} \] a significant difference between the two proportions. Because the confidence interval consists \[ \boxed{\text{(entirely of negative values/entirely of positive values)}} \], it appears that the first proportion is \[ \boxed{\text{(less than/greater than/equal to)}} \] the second proportion. There is \[ \boxed{\text{(sufficient/
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