Schadek Silkscreen Printing Inc purchases plastic cups on wh

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 300 cups. He found 15 to be defective.

What is the estimated proportion defective in the population? (Round your answer to 2 decimal places.)

What are the endpoints of a 95 percent confidence interval for the proportion defective. (Round your answers to 3 decimal places.)

Solution

a)
defective(x)=15
Sample Size(n)=300
Sample proportion = x/n =0.05
b)
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval

Confidence Interval = [ 0.05 ±Z a/2 ( Sqrt ( 0.05*0.95) /300)]
= [ 0.05 - 1.88* Sqrt(0) , 0.05 + 1.88* Sqrt(0) ]
= [ 0.026,0.074]