Two types of medication for hives are being tested. The manufacturer claims that
ID: 3067970 • Letter: T
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.
Explanation / Answer
Here we have to test the hypothesis that,
H0 : p1 = p2 Vs H1 : p1 not= p2
where p1 is population proportion of medication B.
p2 is population proportion of medication A.
Assume alpha = level of significance = 0.01
Given that,
x1 = number of adults given medication B still had hives 30 minutes after taking the medication = 12
n1 = total number of adults given medication B still had hives 30 minutes after taking the medication = 200
x2 = number of adults given medication A still had hives 30 minutes after taking the medication = 20
n1 = total number of adults given medication A still had hives 30 minutes after taking the medication = 200
Here we have to test two proportions.
We can use here two proportion z-test.
This is the two tailed test.
We can do this test in TI-83 calculator.
steps :
STAT --> TESTS --> 6:2-PropZTest --> ENTER --> Input all the values --> Select alternative "not=" --> Calculate -->ENTER
Test statistic = -1.47
P-value = 0.1404
P-value > alpha
Accept H0 at 1% level of significance.
And conclude 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.
Type I error = P(reject H0 / H0)
= P(Two proportions are not equal / proportions are equal)
TYpe II error = P(Accept H0 / H1)
= P(Proportions are equal / proportions are not equal)
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