Question

Schadek Silkscreen Printing, Inc., purchases plastic cups on which to print logos for sporting events, proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large shipment this morning. To ensure the quality of the shipment, he selected a random sample of 520 cups. He found 8 to be defective. a. What is the estimated proportion defective in the population? (Round the final answer to 3 decimal places.) Estimated proportion defective b. What are the endpoints of a 80% confidence interval for the proportion defective. (Round the final answers to 3 decimal places.) Endpoints , c. Zack has an agreement with his supplier that he is to return lots that are 10% or more defective. Should he return this lot?

Answer 1

a. Estimated proportion if defective cups in the population = phat= 8/520 = 0.015

b. The end points of 80% CI for population proportion are given by

( phat +/- z(alpha/2) * sqrt(phat(1-phat) /n))

(0.015 +/- z(0.1) *sqrt(0.015*0.985/520) )

(0.015 +/- 1.282*0.005)

(0.008, 0.022)

Since 10% defective proportion is 0.1 which lies in this confidence interval. Thus with 80% confidence zack can return the lot.

I have given my best to solve your problem. Please like the answer if you are satisfied with it. ?