Question

Independent random samples, each containing 50 observations, were selected from two populations. The samples from populations...

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

Homework Answers

Answer #1

Solution :

Given that,

This is the two tailed test .

The null and alternative hypothesis is ,

H0 : P1 = P2

Ha : P1    P2

1 = x1 / n1 = 31 / 50 = 0.62

2 = x2 / n2 = 25 / 50 = 0.5

= (x1 + x2) / (n1 + n2) = (31 + 25) / (50 + 50) = 0.56

1 - = 0.44

Z = (1 - 1) / * (1 - ) (1 / n1 + 1 / n2)

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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