Question

A very large trial was conducted to combat the Human Papillomavirus (HPV) on 402,245 consenting adults. 201,867 of the patients were given an experimental vaccine (the treatment group), and 200,378 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. (Follow all 5 steps in directions.) Note: all requirements are met - the sample proportions are from two independent, simple random samples, and there are at least five successes and five failures.

Answer 1

H0: Null Hypothesis: P1 - P2 0

HA: Alternative Hypothesis: P1 - P2 < 0

n1= 201,867

p1 = 41/201,867 = 0.0002031

n2 = 200,378

p2 = 124/200,378 = 0.0006188

So,

Q = 1 - P = 0.9995898

Test ststistic is:

Z = (0.0002031 - 0.0006188)/0.00006386 = - 6.5096

= 0.05

One Tail - Left Side Test

From Table,critical value of Z = - 1.645

Since calculated value of Z = - 6.509 is less than critical value of Z = - 1.645, thedifference is significant. Rject null hypothesis.

Conclusion:

The data support the claim that this vaccine is effective.

(b)

= 0.05

From Table, critical values of Z = 1.96

Confidence Interval:

(0.0002031 - 0.0006188) (1.96 X 0.00006386)

= - 0.0004157 0.00001252

= ( - 0.0004282, - 0.0004032)