Question

A manufacturer of a new medication on the market for Crohn's disease claims that the medication is effective in 85% of people who have the disease. One hundred seventy-five individuals with Crohn's disease are given the medication, and 135 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 85% claim the company is making? Make sure to include parameters, conditions, calculations, and a conclusion in your answer. Show all formulas and equations in the working and label.

Answer 1

Given n = 175, X = 135

P bar = X/n = 135/175 = 0.7714

Hypothesis:

Ho:p = 0.85

Ha: p < 0.85(left tail)

Rejection region:

α = 0.05

Zc = −1.64

If Z stat < −1.64, reject H0

Test:

Z stat =(P bar - P)/SQRT(P(1-P)/n) = (0.7714 - 0.85)/SQRT(0.85*(1-0.85)/175)

Z stat = −2.911

Decision:

Z stat = −2.911 < Zc​ = −1.64, reject H0

P value = 0.0018

P value < 0.05, reject H0

Conclusion:

There is enough evidence to conclude that the effectiveness is less than the 85% at 5% significance level