Question

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5% significance level.

Test H0: p = 0.25 vs Ha: p < 0.25 using the sample results p(hat) = 0.15 with n = 102
Round your answer for the test statistic to two decimal places, and your answer for the p-value to three decimal places.

Answer 1

Test statistic = - 2.33

Pvalue = 0.010 (3 decimal places)

Explanation:

Given :

H0: p = 0.25 vs Ha: p < 0.25

Phat = 0.15

Sample size, n = 102

α = 0.05

The test statistic :

(Phat - p) / (√p(1 - p) /n)

1 - p = 1 - 0.25 = 0.75

(0.15 - 0.25) / (√0.25(0.75) /102)

-0.1 / √0.0018382

-0.1 / 0.0428742

Test statistic = - 2.33

The Pvalue using the test statistic score obtained :

P(Z < - 2.33) = 0.0099031 = 0.010

Pvalue < α ; Reject H0