Company A makes a large shipment to Company B Company B can

Company A makes a large shipment to Company B. Company B can reject the shipment if they can conclude that the proportion of defective items in the shipment is larger than 0.1. In a sample of 400 items from the shipment, Company B finds that 59 are defective. Conduct the appropriate hypothesis test for Company B using a 0.05 level of significance.

a) What are the appropriate hypotheses?

A.)H₀: p = 0.1 versus H_a: p > 0.1

B.)H₀: = 0.1 versus H_a: > 0.1    

C.)H₀: p = 0.1 versus H_a: p < 0.1

D.)H₀: p = 0.1 versus H_a: p 0.1

b) What is the test statistic? Give your answer to four decimal places.  

c) What is the critical point for the test? Give your answer to four decimal places.  

d) What is the appropriate conclusion?

A.)Conclude that the defective proportion in the shipment is greater than 0.1 because the test statistic is larger than the critical point.

B.)Fail to reject the claim that the defective proportion in the shipment is 0.1 because the test statistic is larger than the critical point.     

C.)Fail to reject the claim that the defective proportion in the shipment is 0.1 because the test statistic is smaller than the critical point.

D.)Conclude that the defective proportion in the shipment is greater than 0.1 because the test statistic is smaller than the critical point.

Solution

(a)

H0: p = 0.1
Ha: p> 0.1 option A.

(b) p-hat =59/400 = 0.1475

z-test statistic = (0.1475-0.1)/(0.1*0.9/400)^(1/2) = 3.1667
(c) alpha = 0.05

critical value at 0.05(right tailed test ) = 1.645

(d). Reject H0

A.)Conclude that the defective proportion in the shipment is greater than 0.1 because the test statistic is larger than the critical point.