Question

X) 10.2.9 Test the hypothesis using the classical approach and the P-value approach P0.90 Ho p 0.90 versus H1 n= 150, x= 125, ?= 0.05 (a) Perform the test using the classical approach. Choose the correct answer below. Do not reject the null hypothesis. There is not enough information to test the hypothesis. yReject the null hypothesis. (b) Perform the test using the P-value approach. P-value = (Round to four decimal places as needed )

Answer 1

Solution :

Given that,

n =150,

x = 125

$\hat p$ = x / n = 125 / 150 = 0.833

P₀ = 0.90

1 - P₀ = 1 - 0.90 = 0.10

$\alpha$ = 0.05

nP₀ (1 - P₀) = 0.90 * 0.10 = 0.900

z = $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.833 - 0.90 / [$\sqrt$(0.90 * 0.10) / 150

= - 2.73

This is the left tailed test .

P(z <-2.73 ) = 0.0032

Pvalue = 0.0032

Here p-value < $\alpha$

Reject the null hypothesis , because the P-value is Less than.