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 is less than 0.10, she will reject the shipment. To reach a decision, she will test the following hypotheses: H0: p = 0.10, Ha: p < 0.10 To do so, she selects an SRS of 150 potatoes from the more than 3000 potatoes on the truck. Suppose that six of the potatoes sampled are found to have major defects. Reference: Ref 8-5 Based on the test, which of the following conclusions should the inspector draw? There is not statistically significant evidence that too many potatoes are of unacceptable quality so the shipment should not be rejected. There is not statistically significant evidence that the shipment meets the required quality standard so the shipment should be rejected. There is statistically significant evidence that too many potatoes are of unacceptable quality so the shipment should be rejected. There is statistically significant evidence that the shipment meets the required quality standard so the shipment should not be rejected.

Explanation / Answer

In this question the inspector clearly states that - unless there is a clear evidence that proportion of defects in the shipment is < 0.1, the inspector is going to reject the shipment.

He test the H0 = 0.1. NULL Hypothesis. It means that he assumes that the lot of potatoes has 0.1 proportion defects. There is no significant difference that the defects are not = 0.1

H1 < 0.1 Alternate Hypothesis. It means that there is no evidence to accept the NULL hypothesis that the lot of potatoes has p=0.1.

Since p = 6/150 = 0.04 which is < 0.1 Hence we reject the H0. Hence there is no evidence to accept H0.

Hence he will conclude that - There is not statistically significant evidence that too many potatoes are of unacceptable quality so the shipment should not be rejected.

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