Question

#3

A group conducted a randomized experiment to see if hormone therapy was helpful for post-menopausal women The women were randomly assigned to receive a hormone or a placebo After 5 years, 119 of the 8589 on the hormone therapy developed cancer and 83 of the 8437 in the placebo group developed cancerIs this a significant difference? Complete parts a through c below a. State the assumptions and the hypotheses What assumptions about the two samples are necessary to be significance test? OA. The samples are independent, random, and selected from a population that is approximately normal OB. The samples are independent, random, and selected from a populations that have the same standard deviation OC. The samples are independent, random, and a point estimate of the population proportion is known OD. The response variable is categorical, and the samples are independent, random, and large enough Letp represent the probability that someone gets cancer. Let p, represent the probability that a person who receives hormone therapy gets cancer, and let 2 represent the probability that a person who receives a placebo gets cancer. Write the claim as a hypothesis test Choose the correct null and alternative hypotheses below O A. Ho: PDy versus H, P, P2 O B. Ho: P1 P2 versus H, P, P2 O C. Ho: P, D, versus H P P2 OD. HO P = 0 versus H P +0 b. Find the test statistic and the P value and interpret Find the test statistic Click to select your answer

Answer 1

For Sample 1:

n1 = 8589

x1 = 119

p̂1 = x1/n1 = 0.0139

For Sample 2:

n2 = 8437

x2 = 83

p̂2 = x2/n2 = 0.0098

a)

The samples are independent, random and selected from population that is approximately normal.

--

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 ≠ p2

b)

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (119+83)/(8589+8437) = 0.0119

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.0139 - 0.0098)/√[0.0119*0.9881*(1/8589+1/8437)] = 2.42

p-value = 2*(1-NORM.S.DIST(ABS(2.4206), 1)) = 0.015

Answer D.

c)

Conclusion:

Answer D. Do not reject.