Question

Name: 1. Suppose that 1000 customers are surveyed and 850 are satisfied or very satisfied with a corporation's products and services. You want to test the hypothesis Ho: p = 0.9 against H:p 70.9 at the significance level of 0.05. (a) Find the critical region and make a decision. (b) Calculate the P-value for this test and make a decision.
SHOW ALL WORK AND CLEARLY SHOW ANSWERS FOR A AND B!

Answer 1

(a)

$\alpha$ = 0.05

From Table, critical values of Z = $\pm$ 1.96

Critical Region is given by:

R = { Z | Z < - 1.96 OR Z > 1.96}

n = Sample Size = 1000

p = Population Proportion = 0.9

$\hat{p}$ = Sample Proportion = 0.85

SE =

Vpq/n V0.9 x 0.1/1000 0.009487

Test Statistic is given by:

Z = (0.85 - 0.90)/0.009487

= - 5.2705

Since calculated value of Z = - 5.2705 is less than critical value of Z = - 1.96, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the population proportion is not 0.9.

(b)

Table of Area Under Standard Normal Curve gives area = 0.5 nearly.

So,

p - value = (0.5 - 0.5 nearly) X 2

            = 0.0000

Since p - value = 0.0000 is less than $\alpha$ = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the population proportion is not 0.9.