Question

8) Test the hypothesis using the P-value approach.

Answer 1

Step 1:

Ho: p = 0.74

Ha: p $\neq$ 0.74

Step 2: test statistics

n = 500

x = 360

$z = \frac{x - np}{\sqrt{np(1-p)}} = \frac{360 - 500* 0.74}{\sqrt{500* 0.74 (1-0.74)}}$

z = -1.020

p value = 2 * P( Z < - 1.020) = 2 * 0.1539 = 0.3078

Step 3:

alpha = 0.05

The z-critical values for a two-tailed test, for a significance level of α=0.05

zc = −1.96 and zc = 1.96

As the z stat does not fall in the rejection region, we fail to reject the Null hypothesis.

Also as the p value is greater than alpha (0.05) , we fail to reject the Null hypothesis.