Question

Conduct the following test at the

α =0.10

level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume that the samples were obtained independently using simple random sampling.

Test whether

p1≠p2.

Sample data are

x1=28

n1=255​,

x2=36​,

and n2=301.

Answer 1

Solution :

Given that,

(a)

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ : P₁ = P₂

H_a : P₁    P₂

₁ = x₁ / n₁ = 28 / 255 = 0.1098

₂ = x₂ / n₂ = 36 / 301 = 0.1196

= (x₁ + x₂) / (n₁ + n₂) = (28 + 36) / (255 + 301) = 0.1151

1 - = 0.8849

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

Z = (0.1098 - 0.1196) / 0.1151 * 0.8849 (1 / 255 + 1 / 301)

Z = -0.3607

(b )

Test statistic = -0.3607

(c)

P-value = 0.7183

P-value > 0.10

Fail to reject the null hypothesis .