Question

A very large trial was conducted to combat the Human Papillomavirus (HPV) on 401,245 consenting adults. 200,267 of the patients were given an experimental vaccine (the treatment group), and 200,978 of them were administered placebos (the placebo group). In the treatment group 41 people contracted HPV, and in the placebo group 124 people contracted HPV. a) Use a 5% significance level to test the claim that this vaccine is effective, and b) create a confidence interval for testing. (Demonstrate all 5 hypothesis testing steps, with p-values, critical values, and confidence intervals.)

Answer 1

A)Null Hypothesis , H₀: The proportion of the two groups donot differ significantly

Alternative Hypothesis,H_a:The proportion for treatment is more than the proportion for placebo group

Level of significance ,

Test statistic is z =

The value of z is 6.4401

The critical value is

p value is .0000

Since p value is less than .05,we reject the null hypothesis and conclude that the vaccine is effective

B)Confidence interval is given as

CI=⎝⎛​p^​1​−p^​2​−zc​N1​p^​1​(1−p^​1​)​+N2​p^​2​(1−p^​2​)​) =(-.001,0)