Final answer:
To test the claim that more than half of all users of an allergy drug experience relief, we establish a null hypothesis that the proportion is half or fewer, and an alternative hypothesis that it is more than half. We calculate the test statistic using the sample proportion and compare the p-value to the significance level. If the p-value is less than 0.01, we reject the null hypothesis and conclude the alternative hypothesis is likely true.
Step-by-step explanation:
A. The null hypothesis (H0) is that half or fewer subjects experience significant relief from their symptoms using the drug, which can be stated as H0: p ≤ 0.5. B. The alternative hypothesis (Ha) is that more than half of the subjects experience significant relief, stated as Ha: p > 0.5.
C. The random variable, P', represents the sample proportion of subjects experiencing relief. D. To calculate the test statistic, we use the formula for a one-sample z-test for proportions: z = (P' - p0) / sqrt[p0(1 - p0) / n], where P' is the sample proportion, p0 is the proportion from the null hypothesis, and n is the sample size. E. The p-value corresponds to the probability of obtaining a test statistic as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true.
F. If the p-value is less than the significance level (α = 0.01), we reject the null hypothesis. G. A Type I error would occur if we reject the null hypothesis when it is actually true. H. A Type II error would occur if we fail to reject the null hypothesis when the alternative hypothesis is true.
To draw a conclusion, compare the p-value with the significance level. If the p-value < α, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than half of the users experience relief from their symptoms.