Question

A certain drug is used to treat asthma. In a clinical trial of the​ drug, 21 of 299 treated subjects experienced headaches​ (based on data from the​ manufacturer). At a significance level of 0.05, test the claim that less than 9% of people being treated with the asthma drug experience headaches. Use the P-Value method. Address each of the following questions:

Is this a Is this a left tailed, right tailed or two tailed test?

Are there any conditions that must be met before you can solve this problem?

What is alpha?

What is the Null and Alternative hypothesis?

What formula did you use and what is the test statistic?

What is your decision and what P-Value did you use?

In simple terms state the final conclusion that addresses the original claim.

Answer 1

This is a left tailed test

• The sample must be reasonably random
• The sample must be less than 10% of the population
• The sample must be large enough so that:
n• pˆ and n(1 - pˆ ) ≥ 10 for a confidence interval
n• p and n(1 - p) ≥ 10 for the significance test

alpha = 0.05

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.09
Alternative Hypothesis, Ha: p < 0.09

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.0702341137123746 - 0.09)/sqrt(0.09*(1-0.09)/299)
z = -1.19

P-value Approach
P-value = 0.117
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that less than 9% of people being treated with the asthma drug experience headaches.