Question

Make sure you include all the five steps in the hypothesis testing questions.

1. Given n=400 and p=0.3 , perform the following test:

H_0:π = 0.6 Vs H_1:π ≠ 0.6. Use the p-value approach with a significance level of α=0.05.

Answer 1

Solution:

A)

The null and alternative hypothesis are

H₀ : = 0.6 vs H_a :    0.6

B)

Given

n = 400

= 0.3

The test statistic z is

z =

=  (0.3- 0.6)/[0.6*(1 - 0.6)/400]

= -12.25

C)

sign in Ha indicates that the test is TWO TAILED

For TWO TAILED test ,

p value = P(Z < -z) + P(Z > +z) = P(Z < -12.25) + P(Z > +12.25) = 0.0000+0.0000 = 0.0000

The​P-value for this hypothesis test is  0.0000

D)Decision:

reject the null hypothesis H₀

(Because p value is greater than given significance level 0.05)

E) Conclusion:

There is sufficient evidence to conclude that the population proportion is different from 0.6