Independent random samples, each containing 50 observations, were selected from two populations. The samples from populations 1 and 2 produced 31 and 25 successes, respectively. Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.05.
(a) The test statistic is
(b) The P-value is
Solution :
Given that,
This is the two tailed test .
The null and alternative hypothesis is ,
H_{0} : P_{1} = P_{2}
H_{a} : P_{1} P_{2}
_{1} = x_{1} / n_{1} = 31 / 50 = 0.62
_{2} = x_{2} / n_{2} = 25 / 50 = 0.5
= (x_{1} + x_{2}) / (n_{1} + n_{2}) = (31 + 25) / (50 + 50) = 0.56
1 - = 0.44
Z = (_{1} - _{1}) / * (1 - ) (1 / n_{1} + 1 / n_{2})
Z = (0.62 - 0.5) / 0.56 * 0.44 * (1 / 50 + 1 / 50)
Z = 1.209
Test statistic = 1.21
P(z > 1.21) = 0.1131
P-value = 2 * 0.1131 = 0.2262
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