Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test.

Upper H 0 : p = 0.89 versus Upper H 1 : p not equals 0.89

n=500, x=430, a=0.01

Now find p ^  (Type an integer or a decimal. Do not​ round.)

Find the test statistic z0. (Type an integer or a decimal. Do not​ round.)

Find P-value (Type an integer or a decimal. Do not​ round.)

Answer 1

Solution :

Given that,

= 0.89

1 - = 0.11

n = 500

x = 430

Level of significance = = 0.01

Point estimate = sample proportion = = x / n =430 / 500 = 0.86

This a two tailed test.

Test statistics

z = ( - ) / *(1-) / n

= ( 0.86 - 0.89) / (0.89*0.11) / 500

= -2.14

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

= 2*P(Z <-2.14 )

=2*0.0162

= 0.0324

The p-value is p =0.0324, and since p = 0.0324 > 0.01, it is concluded that the null hypothesis is not rejected.