Question

You may need to use the appropriate appendix table or technology to answer this question Consider the following hypothesis test H0: p = 0.20 Ha: p # 0.20 A sample of 400 provided a sample proportion p = 0.185 (a) Compute the value of the test statistic. (Round your answer to two decimal places.) (b) What is the p-value? (Round your answer to four decimal places.) p-value- (C) 0.05, what is your conclusion? 0 Reject H0. There is insufficient evidence to conclude that p # 0.20. O Do not reject Ho. There is sufficient evidence to conclude that 0.20 O Do not reject Ho. There is insufficient evidence to conclude that p # 0.20 O Reject HO. There is sufficient evidence to conclude that p 0.20. At α (d) What is the rejection rule using the critical value? (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic s test statistic 2 What is your conclusion? O Reject Ho. There is insufficient evidence to conclude that p 0.20. O Do not reject Ho. There is sufficient evidence to conclude that p 0.20. O Do not reject Ho. There is insufficient evidence to conclude that p # 0.20 O Reject Ho. There is sufficient evidence to conclude that p # 0.20. Need Help?Read ItMaster Talk to a Tutor

Answer 1

a)

Test statistic =

P-p 0.185-0.2 ー-0.75 0.2(1-0.2) 400 7t

b)

Since this is a two tailed test, so the p value is given by:

c)

2 × P(Z < -0.75)-2 × P(Z > 0.75) 2 ×「1-0.77337| 0.45326 0.4533 2 × [1-P(Z < 0.75)] =

Since p-value is greater than 0.05, so we do not have sufficient evidence to reject H0.

Thus we do not reject H0.

Hence 3rd option is the correct option.

d)

The critical values are:

$-Z_{\alpha/2}=-Z_{0.05/2}=-Z_{0.025}=-1.96$ and

a/2-40. 05/2 20,025 1.96

Rejection rule:

Test statistic < -1.96 or Test statistic > 1.96

Since test statistic does lie in the rejection region, so we do not have sufficient evidence to reject H0.

Thus we do not reject H0.

Hence 3rd option is the correct option.