We wish to test the hypothesis H0:  p1-p2 = 0 versus the hypothesis H1: p1 - p2  0 at a 5% level of significance.  Here, p1 denotes, of all bolts manufactured on Machine A, that fraction that are defective, and p2 denotes, of all bolts manufactured on Machine B, that fraction which consists of defective bolts.  In order to test these hypotheses, we obtain a random sample of 400 bolts manufactured on Machine A, and independently, we obtain a random sample of 400 bolts from Machine B.  Of the bolts from the Machine A  sample, we find that 20 are defective, whereas for the Machine B sample we find that 40 are defective.  Compute the p-value.

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.