Question

on Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.77 versus H, :p*0.77 n=500, x=380. a=0.01 Is npo (1-P) 2 10? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) OA. Yes, because npo (1-Po) - OB. No, because npo (1-P) =

Answer 1

Solution:

Given that,

= 0.77

Po

1 - = 0.23

Po

n = 500

x = 380

Level of significance = $\alpha$ = 0.01

Point estimate = sample proportion = $\hat p$ = x / n = 0.76

A) Yes, because nP₀( 1 - P₀) = 88.55

This is a two tailed test,

Test statistics

z = ($\hat p$ -
Po
) / $\sqrt{}$
Po
*(1-
Po
) / n

= ( 0.76 - 0.77) / $\sqrt{}$ (0.77*0.23) / 500

= -0.53

P-value = 2 * P(Z < -0.53 )

= 0.5952

Since, P-value = 0.5952 > 0.01, it is concluded that fail to reject H0.