Question

Perform the following hypothesis test of a proportion:

H_O: p = 0.33

H_A: p not equal to 0.33

The sample proportion is 0.31 based on a sample size of 100. Use a 10% significance level.

A) What is the value of the test statistic? (Give answer rounded to 2 decimals) (be careful to make sure your + or - sign is correct)

B) What is the p-value for the problem?

C) should the null hypothesis be rejected? YES or NO

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.33

H_a : p 0.33

= 0.31

n = 100

P₀ = 0.33

1 - P₀ = 0.67

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.31 - 0.33 / [(0.33 * 0.67) / 100]

= -0.43

P(z < -0.43) = 0.3336

P-value = 2 * 0.3336 = 0.6672

= 0.10

P-value >

Fail to reject the null hypothesis .

No