Question

(7) Find (a) the test statistics CT.S.) and (b) IP-value used to test the claim : P = P2. (comparing two population proportion.) Sample lin,= 173 and x = 59 Sample a na=179 and xa=65 na 7

Answer 1

Solution :

Given that,

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ : P₁ = P₂

H_a : P₁  $\neq$  P₂

$\hat p$₁ = x₁ / n₁ = 59 / 173 = 0.341

$\hat p$₂ = x₂ / n₂ = 65 / 179 = 0.363

$\hat p$ = (x₁ + x₂) / (n₁ + n₂) = (59 + 65) / (173 + 179) = 0.3523

1 - $\hat p$ = 0.6477

Z = ($\hat p$₁ - $\hat p$ ₁) / $\sqrt$ $\hat p$ * (1 - $\hat p$ ) (1 / n₁ + 1 / n₂)

Z = (0.341 - 0.363) / $\sqrt$ 0.3523 * 0.6477 (1 / 173 + 1 / 179)

Z = -0.43

(a) Test statistic = -0.43

(b) P-value = 0.6645