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 will test the hypotheses H 0 : p = 0.10 , H a : p < 0.10 H0:p=0.10,Ha:p<0.10. He selects an SRS of 100 potatoes from the over 2000 potatoes on the truck. Suppose that 6 of the potatoes sampled are found to have major defects. What is the P-value for the test?

Answer 1

Explanation:

Given that 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.

`H 0 : p = 0.10 , \\H a : p < 0.10`

n =100

SE =
`\sqrt{(pq)/(n) } =\sqrt{(0.1*0.9)/(100) } \\=0.03`

Sample P = 6 out of 100 = 0.06

p difference = -0.04

p value = 0.484

Since p value >0.05 we accept null hypothesis