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 . 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. Which of the following is true?

Strictly speaking, the inspector should take a larger sample in order to more safely apply the large sample significance test for proportion.

The inspector might reach the wrong conclusion about the lot of potatoes, whether he returns the shipment or not.

The inspector will decide to reject the shipment because there's weak evidence that the proportion of potatoes with serious defects is less than 0.10.

All of the above statements are true.

Answer 1

solution Here Given Test Ho - P=01 vs HIAPLOI n=100, x=6, 8 = 66 = 0.06 statistic z= p-P = 0.06-01 = -1.33 PQ 0-10.9 (00 P_value =P(22-1:33)=10.0913 - The inspector will decide to reject the rate hypothes shipment because there is weak evidence that the proportion of potatos caith serious defects is x ora less than o. - he might take the larger sample to give proper conclusion - Because of that he might reach wrong conclusion whether he return the shipment or not. - so, all the statements are true (last option)