Because of variability in the manufacturing process, the actual yielding point of a sample of mild steel subjected to increasing stress will usually differ from the theoretical yielding point. Let p denote the true proportion of samples that yield before their theoretical yielding point. If on the basis of a sample it can be concluded that more than 20% of all specimens yield before the theoretical point, the production process will have to be modified.

(a) If 14 of 52 specimens yield before the theoretical point, what is the P-value when the appropriate test is used? (Round your answer to four decimal places.)
P-value = ___

What would you advise the company to do? Choose one below

___Because the P-value is rather small, H0 will be rejected at any reasonable \alpha, so the production process will have to be modified.
___Because the P-value is rather large, H0 would not be rejected at any reasonable \alpha, so the production process will have to be modified.
___Because the P-value is rather large, H0 would not be rejected at any reasonable \alpha, so no modification appears necessary.
___Because the P-value is rather small, H0 will be rejected at any reasonable \alpha, so no modification appears necessary.

(b)Besides using the p-value approach above, use the "rejection region" approach to perform a test of hypotheses about the true (population)proportion. Use \alpha = 0.05. .