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 H 0 : 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.Compute the value of the large-sample z statistic.What is the P-value for this hypothesis test?

A) Less than 0.0002
B) 0.0098
C) 0.0284
D) 0.0568

James Crumsey · Accepted Answer

Final Answer : C, Explanation :  The sample proportion of major defects is 8/150 = 0.0533.The null hypothesis is p = 0.10 and the alternative hypothesis is p < 0.10.The standard error of the proportion is sqrt((0.10*(1-0.10))/150) = 0.0275.The Z-score is (0.0533 - 0.10)/0.0275 = -1.7091.Using a standard normal table, the P-value is approximately 0.0284. Therefore, the best choice is C.

Definitions

Learning Objectives

Learning Objectives

Related questions