Question 7 Suppose that the new study uses a level of significance of 0.05 to test the claim in Question 6. The probability of Type I error is 0.025 0.05 0.95 0.975 Question 8 Based on previous studies of school children who were vaccinated and contracted the flu, the time in hours that the flu symptoms last is assumed to follow a normal distribution with a mean of 20.7 hours and a standard deviation of 7.3 hours. The probability that a randomly selected school child has flu symptoms for more than 24 hours is 0.1628 0.3256 0.6744 0.8372
DO QUESTION 7 AND 8 ONLY
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>0.5 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
Question 7
Suppose that the new study uses a level of significance of 0.05 to test the claim in Question 6. The probability of Type I error is
0.025
0.05
0.95
0.975
Question 8
Based on previous studies of school children who were vaccinated and contracted the flu, the time in hours that the flu symptoms last is assumed to follow a
0.1628
0.3256
0.6744
0.8372
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