Question

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 11 of 48 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?

Because the P-value is rather large, H₀ would not be rejected at any reasonable α, so the production process will have to be modified.

Because the P-value is rather small, H₀ will be rejected at any reasonable α, so no modification appears necessary.    

Because the P-value is rather large, H₀ would not be rejected at any reasonable α, so no modification appears necessary.

Because the P-value is rather small, H₀ will be rejected at any reasonable α, so the production process will have to be modified.

(b) If the true percentage of "early yields" is actually 50% (so that the theoretical point is the median of the yield distribution) and a level 0.01 test is used, what is the probability that the company concludes a modification of the process is necessary? (Round your answer to four decimal places.)

Answer 1