An inspector inspects large truckloads of potatoes to determine the proportion p

Question

An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion, p, is less than 0.10, he will reject the shipment. He selects a random sample of 200 potatoes from the more than 5000 potatoes on the truck. Twelve of the potatoes sampled are found to have major defects. How would you interpret the meaning of this confidence interval?

a. You are 95% certain that the true population of defective potatoes lies somewhere between the lower bound and the upper bond of the confidence interval.

Explanation / Answer

Given the values , first we will calculate the interval

p = 12 / 200 = 0.06 q = 0.94

p = 200/5000 = 0.04

z = p - p / sqrt pq/n

z =( p - 0.06)/ 0.055

z = 1.96

0.06 -1.96*0.055<p<0.06 -1.96*0.055

0.04 <p <0.06

hence p lies between 0.04 and 0,06

The the prob p plies in interval is 0 or 1

so d) is the correct answer

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