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 600 cups. He found 28 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 90% 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?

(Click to select)  No, lot not 10% defective.  Yes, 28 is outside the confidence interval.  Yes, the lot is 10% defective.

Answer 1

a)

sample proportion, = 0.047

b)

sample size, n = 600
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.047 * (1 - 0.047)/600) = 0.0086

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

Margin of Error, ME = zc * SE
ME = 1.64 * 0.0086
ME = 0.0141

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.047 - 1.64 * 0.0086 , 0.047 + 1.64 * 0.0086)
CI = (0.033 , 0.061)

c)

Yes, the lot is 10% defective.