Question

Researchers want to test the effectiveness of a new anti-anxiety medication. In clinical testing, 64 out of 200 people taking medication report symptoms of anxiety. Of the people receiving a placebo, 92 out of 200 report symptoms of anxiety. Is the medication working any differently than the placebo ? Test this claim using alpha = 0.05 Perform all steps of Hypothesis testing, including P-Value reaffirmation test.

Answer 1

Answer)

Null hypothesis Ho : P1 = P2

Alternate hypothesis Ha : P1 < P2

N1 = 200, P1 = 64/200

N2 = 200, P2 = 92/200

First we need to check the conditions of normality that is if n1p1 and n1*(1-p1) and n2*p2 and n2*(1-p2) all are greater than equal to 5 or not

N1*p1 = 64

N1*(1-p1) =136

N2*p2 = 92

N2*(1-p2) = 108

All the conditions are met so we can use standard normal z table to conduct the test

Test statistics z = (P1-P2)/standard error

Standard error = √{p*(1-p)}*√{(1/n1)+(1/n2)}

P = pooled proportion = [(p1*n1)+(p2*n2)]/[n1+n2]

After substitution

Test statistics z = -2.87

From z table, P(Z<-2.87) = 0.0021

So, P-Value = 0.0021

As the obtained P-Value is less than the given significance 0.05

We reject the null hypothesis

And we have enough evidence to conclude that it is effective