an 0.5. Assume that p is the population proportion of vaccinated high school children who contract the flu. The appropriate framework to test the new study's claim is H0:p>0.5 vs H1:p<0.5 H0:p=0 vs H1:p≠0
do question 4, 5 and 6 only
The new study claims that the probability of contracting the winter flu among vaccinated high school children is less than 0.5. Assume that p is the population proportion of vaccinated high school children who contract the flu. The appropriate framework to test the new study's claim is
H0:p>0.5 vs H1:p<0.5
H0:p=0 vs H1:p≠0
H0:p=0 vs H1:p>0
H0:p=0.5 vs H1:p<0.5
Question 4
The new study takes a random sample of 14 vaccinated high school children. Let x be the number of children in the sample who contract the flu. The p-value for the test can be calculated from a Binomial distribution using P(X≤x). The maximum number of children who can contract the flu to give evidence against the null hypothesis in Question 3 at the 5% level is
1
2
3
5
Question 5
Suppose the actual population proportion of vaccinated high school children who contract the flu is 30%. For a random sample of 14 vaccinated high school children and based on your answer to Question 4, the probability of making a Type II error is
0.3637
0.6448
0.8392
0.8631
Question 6
The new study also carried out a test to determine whether the population proportion of unvaccinated school children contracting winter flu was higher than the population proportion of vaccinated school children. The Z test statistic to test this belief is found to be 1.874. The corresponding p-value is
0.0305
0.1212
0.3036
0.7724
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