In a clinical study of an allergy drug, 103 of the 202 subjects reported experie
ID: 3313447 • Letter: I
Question
In a clinical study of an allergy drug, 103 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief.
1. Identify the claim, and write the claim, the null hypothesis, and the alternative hypothesis in symbolic form.
2. Determine if the test is two-tailed, right-tailed, or left-tailed, and determine the value of the test statistic.
3. Find the P-value, and use it to either reject or fail to reject the null hypothesis.
4. Write your conclusion in a complete sentence in plain English.
Explanation / Answer
Solution:
1) Given that x = 103, n = 202
sample proportion p = x/n = 103/202 = 0.5099
The null hypothesis is: H0: p = 0.5
and the alternative hypothesis is: Ha: p > 0.5
2) The test statistic is z = (p - p0)/(p0(1-p0)/n)
= (0.5099- 0.5)/ (0.5(1-0.5)/202)
= 0.2814
3) P-value = 0.3892
Since the P-value is greater than the significance level 0.01, we cannot reject the null hypothesis.
4)This means that at the 0.01 significance level, we cannot support the claim that more than half of all those using the drug experience relief.