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 H0: p = 0.10, Ha: p < 0.10. He selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Suppose that 12 of the potatoes sampled are found to have major defects. The P-value of this test is:

(1)  

Replacing the info given we got:

And the p value would be given by:

Step-by-step explanation:

Information given

n=200 represent the random sample taken

X=12 represent the potatoes with major defects

estimated proportion of potatoes with major defects

is the value that we want to test

z would represent the statistic

represent the p value

Hypothesis to test

We want to check if the true proportion is less than 0.10 so then the system of hypothesis are:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Replacing the info given we got:

And the p value would be given by: