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 Which of the following assumptions for inference about a proportion, using a hypothesis test, are violated? n is so large that both np0 and n(1 – p0) are 10 or more, where p0 is the proportion with major defects, if the null hypothesis is true. The population is at least 10 times as large as the sample. The data are an SRS from the population of interest. There appear to be no violations.

Explanation / Answer

H0: p = 0.10, Ha: p < 0.10

Sample proportion p0 = 6/150 = 0.04

Assumptions: i) np0 = 150*0.04 = 6 < 10 and ii) n(1-p0) = 150*(1-0.04) = 146 > 0

Normality condition is not satiesfied

Test Statsitic

Z = (0.04 - 0.10) / sqrt( 0.10 * 0.90 / 150)

= -0.06 / 0.0245 = -2.45

Critical value of Z is -1.645

Here Z value < Z critical value so we reject H0

thus we conclude that p < 0.10

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