Question

Two types of medication for hives are being tested to determine if there is a difference in the proportions of adult patient reactions. Twenty out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. Twelve out of another random sample of 180 adults given medication B still had hives 30 minutes after taking the medication. Test at a 1% level of significance.

1) For this hypothesis test, the null and alternative hypotheses would be:

2)State the null hypothesis as a complete sentence:

3)State the alternative hypothesis as a complete sentence:

4)State the null and alternative hypothesis as a difference statement

5)This test would require a  _________ test.

6)How could you rewrite the claim to be a left-tail test?

7)Determine the point estimator of drug A

8)Determine the point estimator of drug B

9)Determine the test statistic

10)Determine the p-value

11)Determine the significance level as a decimal number.

12)What would be your formal conclusion?

13)What practical conclusion can we make about the claim? (In a complete sentence)

Answer 1

1) For the given test, the null and alternative hypotheses would be H0: p1 = p2 vs H1: p1 p2 where p1, p2 are the proportions of adults having hives after taking the medication using medicine A and B respectively.

2) The null hypothesis is that, there is no difference in the proportions of adult patient reactions for two different types of medication.

3) The alternative hypothesis is that, there is significant difference in the proportions of adult patient reactions for two different types of medication.

4) The null and alternative hypothesis as a difference statement can be written as:

H0: p1 - p2 = 0 vs H1: p1 - p2 0

5) The test would require a two tailed test, since here only the presence of difference is to be tested.

6) The claim in terms of left tailed test is to be written as--

H0: p1 = p2 vs H1: p1 < p2

7) The sample proportion is a point estimator of the population proportion. Thus,  the point estimator of drug A = 20/200 = 0.1

8)  The point estimator of drug B = 12/180 = 0.067

9) The test statistic for the given problem is Z = (p1 - p2) / SE where
p1 is the sample proportion from population 1, p2 is the sample proportion from population 2.

SE = standard error (SE) of the sampling distribution difference between two proportions.

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }, where p is the pooled  sample proportion.

p = (p1 * n1 + p2 * n2) / (n1 + n2) where n1,and n2 are the sample sizes respectively.

Here, p1 = 0.1, p2 = 0.067, n1 = 200, n2 = 180, p =0.08421 , SE = 0.0285313

Thus, the test statistic is Z = 1.168308

10) The p-value is the probability of finding a more extreme value than the observed test statistic assuming the null hypothesis is true. Here, p-value is =  0.2426827

11) The significance level = 1/100 = 0.01

12) The formal conclusion is that we fail to reject H0 since the p-value is greater than the significance level.

13) Using a 1% level of significance, we can say that there is no significant difference in the proportions of adult patient reactions for two different types of medication.