A new study to determine the effectiveness of winter flu vaccinations measures the benefits of a flu shot for school children. The study comprises two random samples of school children who were vaccinated. One sample is from a primary school and the other from a high school.

Question 1

According to previous studies, 50% of vaccinated primary school children contract winter flu. If a study takes a random sample of 18 vaccinated primary school children, the probability that less than 4 children in the sample contract flu is

0.0038

0.0117

0.0154

0.6439

Question 2

For the random sample in Question 1, the probability that at least 4 children but no more than 8 children contract flu is

0.0154

0.2366

0.4035

0.5713

Question 3

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>0.5vsH1:p<0.5

H0:p=0vsH1:p0

H0:p=0vsH1:p>0

H0:p=0.5vsH1: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(Xx). 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