Because of variability in the manufacturing process the actu

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 = 1

Solution

It is a right-tailed test.

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(14/52-0.2)/sqrt(0.2*0.8/52)

=1.25

So the p-value= P(Z>1.25) =0.1056 (from standard normal table)