Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test. Upper H 0 : p = 0.5 versus Upper H 1 : p < 0.5 n=250, x=130, α=0.01 What is the P-value?

calculate the test statistic z0

identify the p-value

Choose the correct result of the hypothesis test for the​ P-value approach below.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p < 0.50

n = 250

x =130

= x / n = 130 / 250 =0.52

P₀ = 0.50

1 - P₀ = 1 - 0.50 = 0.50

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.52 - 0.50 / [(0.50*0.50) / 250 ]

= 0.63

Test statistic = z = 0.63

P(z < 0.63 ) = 0.7357

P-value = 0.7357

= 0.01

P-value >

0.7357 > 0.01

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that