Two types of medication for hives are being tested. The manufacturer claims that

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.

Explanation / Answer

Let p(1)=true proportion of people that still had hives 30 mintues after taking medicine A

Let p(2)=true proportion of people that still had hives 30 mintues after taking medicine B

Sample X N Sample p(i)
1 20 200 0.100000
2 12 200 0.060000

Difference = p (1) - p (2)
Estimate for difference: 0.04
Test for difference = 0 (vs < 0): Z = 1.47 P-Value = 0.930>0.01

Hence we fail to reject H0:difference (p(1)-p(2))=0 at 0.01 level and committed Type II error.

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