 From Mathematics, Statistics
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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 HPVcaused cervical cancer. Of 8460 women given Gardasil, none developed HPVcaused 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 HPVcaused cervical cancer.
 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 pvalue 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 
 Perform a hypothesis test the following statement
 Smooth coats are more common among black mice than among grey mice”
Pr(SB)>Pr(SG)
 Smooth coats are more common among black mice than among grey mice”
 Perform a hypothesis test for the following statement
 Smooth coats are more common than wavy coats”
Pr(S)>Pr(W)
 Smooth coats are more common than wavy coats”
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 Submitted On 09 Apr, 2015 01:24:39
 Smartwriter
 Rating : 5
 Grade : A+
 Questions : 4
 Solutions :163
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 Earned : $2691.05