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.If there is clear evidence that this proportion is less than 0.10,she will accept the shipment.To reach a decision,she will test the hypotheses H₀: p = 0.10 versus H_a: 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.If there is clear evidence that this proportion is less than 0.10,she will accept the shipment.To reach a decision,she will test the hypotheses H₀: p = 0.10 versus H_a: p < 0.10.To do so,she selects a simple random sample of 150 potatoes from the more than 3000 potatoes on the truck.Only 8 of the potatoes sampled are found to have major defects.What is the value of the large-sample z statistic? A)z = -2.33 B)z = -1.91 C)z = 2.33 D)z = 1.91

Quizplus · Accepted Answer

The sample proportion of major defects is:

phat = 8/150 = 0.0533

The standard error for the sample proportion is:

SE(phat) = sqrt[p(1-p)/n] = sqrt[0.1(0.9)/150] = 0.0279

The z statistic is:

z = (phat - p) / SE(phat) = (0.0533 - 0.1) / 0.0279 = -1.91

Therefore, the answer is (B).

An Inspector Inspects Large Truckloads of Potatoes to Determine the Proportion