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Question
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Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
a) Null hypothesis: P1 = P2
b) Alternative hypothesis: P1 P2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. 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 = 0.06775
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.0195
c)
z = (p1 - p2) / SE
z = - 3.05
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 two-tailed test, the P-value is the probability that the z-score is less than - 3.05 or greater than 3.05.
d) Thus, the P-value = 0.0011
Interpret results. Since the P-value (0.0011) is less than the significance level (0.01), we cannot accept the null hypothesis.
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