In a winter of an epidemic flu, the parents of 2000 babies were surveyed by rese
ID: 3251204 • Letter: I
Question
In a winter of an epidemic flu, the parents of 2000 babies were surveyed by researchers at a wellknown pharmaceutical company to determine if the companys new medicine was effective after two days. Among 120 babies who had the flu and were given the medicine, 29 were cured within two days. Among 280 babies who had the flu but were not given the medicine, 56 recovered within two days. Is there any significant indication that supports the companys claim of the effectiveness of the medicine? Use a significance level of 0.05.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: PGiven medicine< PNot medicine
Alternative hypothesis: PGiven medicine > PNot medicine
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.2125
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.01992
z = (p1 - p2) / SE
z = 2.09
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than 0.934. We use the Normal Distribution Calculator to find P(z > 2.09) = 0.0183
Thus, the P-value = 0.0183
Interpret results. Since the P-value (0.0183) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that medicine is effective.
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