Question

Two types of medication for hives are being tested. The manufacturer claims that the new medication B is more effective than the standard medication A and undertakes a comparison to determine if medication B produces relief for a higher proportion of adult patients within a 30-minute time window. 20 out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. 12 out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication. The hypothesis test is to be carried out at a 1% level of significance.

A) Describe an outcome that would result in a Type I error. Explain the rationale for your answer.

B) Describe an outcome that would result in a Type II error. Explain the rationale for your answer.

Answer 1

Solution:

The null and alternative hypotheses for the given test scenario are given as below:

Null hypothesis: H₀: The new medication B is same effective as the standard medication A.

Alternative hypothesis: H_a: The new medication B is more effective than the standard medication A.

A) Describe an outcome that would result in a Type I error. Explain the rationale for your answer.

We know that the type I error is the probability of rejecting the null hypothesis when the null hypothesis is true. For the given scenario, the type I error is the probability of rejecting the null hypothesis that the new medication B is same effective as the standard medication A; however the new medication B is same effective as the standard medication A. This means type I error occurs when we conclude that the new medication B is more effective than the standard medication A, however new medication B is same effective as the standard medication A.

B) Describe an outcome that would result in a Type II error. Explain the rationale for your answer.

We know that the type II error is the probability of do not reject the null hypothesis when the null hypothesis is not true. For the given scenario, the type II error is the probability of do not rejecting the null hypothesis that the new medication B is same effective as the standard medication A; however the new medication B is more effective than the standard medication A. This means type II error occurs when we conclude that new medication B is same effective as the standard medication A, but actually new medication B is more effective than the standard medication A.