Question

In Lesson Ten you’ve worked with techniques for conducting hypothesis tests for two means or two proportions. Work through the following exercise.

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.

State the null and alternative hypotheses in words and in statistical symbols. (3 points)

What statistical test is appropriate to use? Explain the rationale for your answer. (3 points)

Would the test be right-tailed, left-tailed or two-tailed? Explain the rationale for your answer. (3 points)

Describe an outcome that would result in a Type I error. Explain the rationale for your answer. (3 points)

Describe an outcome that would result in a Type II error. Explain the rationale for your answer. (3 points)

Answer 1

(a)
H0: Null Hypothesis: (The new medication B is not more effective than the standard medication A)
HA: Alternative Hypothesis: (The new medication B is more effective than the standard medication A)

(b)

2 Independent Samples t test

Explanation: The Standard Deviations of the two populations are not given.

(c)

Left Tailed test

Explanation:

Alternative Hypothesis has less than sign.

(d)

Type I Error: Rejection of a true null hypothesis.

Suppose in reality the new medication B is not more effective than the standard medication A. But, we wrongly conclude that The new medication B is more effective than the standard medication A. Type I Error is committed in such a situation.

(e)

Type II Error: Failure to reject of a false null hypothesis.

Suppose in reality the new medication B is more effective than the standard medication A. But, we wrongly conclude that The new medication B is not more effective than the standard medication A. Type II Error is committed in such a situation.