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) State the null and alternative hypotheses in words and in statistical symbols.

B) What statistical test is appropriate to use? Explain the rationale for your answer.

C) Would the test be right-tailed, left-tailed or two-tailed? Explain the rationale for your answer.

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

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

Answer 1

A)

Let p1 shows the proportion of adults given medication A get relief 30 minutes after taking the medication and p2 shows the proportion of adults given medication B get relief 30 minutes after taking the medication.

Hypotheses are:

(B)

Since we need to compare two proportion so z test should be used.

(C)

Test is left tailed.

D)

Type I error is the probability of rejecting the true null hypothesis.

That is researcher conclude that medication B produces relief for a higher proportion of adult patients within a 30-minute time window while actually medication B does not produce relief for a higher proportion of adult patients within a 30-minute time window.

E)

Type II error is the probability of fail to reject the false null hypothesis.

That is researcher conclude that medication B does not produce relief for a higher proportion of adult patients within a 30-minute time window while actually medication B produces relief for a higher proportion of adult patients within a 30-minute time window.