Question

Please no cursive

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.

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

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

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

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

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

Answer 1

Given that,

There are two types of medicines A and B.

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.

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

The hypothesis for the test is,

H0: Pa = Pb Vs Pa < Pb

In wording :

H0 : new medication B is less effective than the standard medication A.

H1 : new medication B is more effective than the standard medication A

Assume alpha = level of significance = 1% = 0.01

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

Here we will use two proportion z-test.

Here sample size is 200 which is too large so we will go to tow sample z-test.

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

The test is left tailed and therefore this is one tailed test.

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

Type I error = P(Reject H0 / H0 true)

= P(new medication B is more effective than the standard medication A / new medication B is less effective than the standard medication A.)

Type I error we denote by alpha.

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

Type II error = P(Accept H0 / H1 is true)

= P(new medication B is less effective than the standard medication A. / new medication B is more effective than the standard medication A)

Type II error we denote by beta.