Determine the test statistic. Determine the​ P-value. State the final conclusion that addresses the original claim.

Question

Suppose

211 subjects are treated with a drug that is used to treat pain and

53 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20​% of users develop nausea.

Answer 1

Your null hypothesis Ho: p0 (the proportion than develop nausea) = 0.20

Your alternate hypothesis Ha: p0 > 0.2

You will use a one proportion z-test to verify the claim in the alternative hypothesis.

You first need to compute the sample proportion phat = number who develop nausea/total number of subjects.

You will then need to compute the z-statistic: (phat - p0)/sqrt(p0* (1-p0)/n), where n is the total number of subjects and p0 is the value under the null hypothesis (0.2).

Use the standard normal probability table to compute the probability that z > the above computed z-statistic. That is your p-value. If the p-value is less than 0.01, you can reject the null hypothesis.