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1. Most cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (“Gardasil”) against these HPV strains. Worldwide clinical trials followed young women 16 to 26 years of age after vaccination or administration of a placebo for two to four years for signs of HPV-caused cervical cancer. Of 8460 women given Gardasil, none developed HPV-caused cervical cancer. In contrast, 53 of the 8487 women given a placebo did.

Find a 95% confidence interval for the difference between the two population proportions of women developing HPV-caused cervical cancer.

1.  The accompanying partially complete contingency tables shows the responses to two treatments:

 Treatment 1 2 Response success 70 failure total 100 200

a) Invent a fictitious data set that complete the table above

b) Calculate the sample proportion of success, (success | treatment 1) and (success | treatment 2) for the data set.

c) Compute the test statistic and p-value for the following nondirectionl test.

Ho: The success rate and treatment are independent.

Ha: The success rate and treatment are dependent.

d) Consider the following directional test:

Ho: The success rate of treatment 1 is the same as treatment 2;

Ha: The success rate of treatment 1 is greater than treatment 2.

Do a consistency check for the directional contingency test and show that your sample is ________________(consistent / inconsistent) with Ha, because_____________________________________________________________________

3. Consider a fictitious population of mice. Each animal’s coat is either black (B) or grey(G) in color and is either wavy (W) or smooth (S) in texture. Express each of the following relationships in terms of probabilities or conditional probabilities relating to the population of animals.

.Suppose a random sample of mice is selected from the population and the coat color and texture are observed; consider the accompany partially completed contingency table for the data.

 Color B G Texture W 20 50 S 40 100 total 60 150

1. Perform a hypothesis test the following statement
• Smooth coats are more common among black mice than among grey mice”
Pr(S|B)>Pr(S|G)
2. Perform a hypothesis test for the following statement
• Smooth coats are more common than wavy coats”
Pr(S)>Pr(W)
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