Question

In a clinical study of an allergy drug, 108 of the 200 subjects reported experiencing significant relief from their symptoms. Using a 1% significance level test the claim that more than half of all those using the drug experience relief.

Answer 1

Let p be the true proportion of subjects who experience significant relief from their symptoms.

Null Hypothesis H0: p = 0.50

Alternative Hypothesis Ha: p > 0.50

np(1-p) = 200 * 0.50 * (1 - 0.50) = 50

Since np(1-p) > 10, the sample size is large enough to approximate the sampling distribution of proportion as normal distribution and conduct a one sample z test.

The sample can be assumed to be a random sample, the value of np(1-p) is 50, which is greater than or equal to 10 and the sample size can be assumed to be less than or equal to 5% of the population size of subjects. Thus, all assumptions of one sample z test are satisfied,

Standard error of sample proportion, SE = = 0.03535534

Sample proportion, = 108/200 =  0.54

Test statistic, z = ( - p) / SE = (0.54 - 0.5)/0.03535534 = 1.13

p-value = P(z > 1.13) = 0.1292

Since, p-value is greater than 0.01 significance level, we fail to reject null hypothesis H0 and conclude that there is no significant evidence from the data to support the claim that the true proportion of subjects who experience significant relief from their symptoms.