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

For people taking medication:

Sample size is N1= 200

People report symptoms of anxiety, X1 =64

Sample proportion, = 64/ 200 = 0.32

For people receiving plaebo:

Sample size is N2= 200

People report symptoms of anxiety, X2 =92

Sample proportion, = 92/ 200 = 0.46

(1) Null and Alternative Hypotheses:

(2) Critical value:

At =0.05, and the critical value for a two-tailed test is = 1.96

(3) Test Statistics

(4) Decision about the null hypothesis

Since it is observed that |z| = 2.90 > = 1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0037, and since p = 0.0037 < 0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the medication is working differently than the placebo?, at the 0.05 significance level.