A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 14 of the plates have blistered.
a) Does this provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances? State and test the appropriate hypotheses using a significance level of 0.05.
b) If it is really the case that 15% of all plates blister under these circumstances and a sample of size 100 is used, how likely is it that the null hypothesis of part (a) will not be rejected by the level 0.05 test?
c) How many plates would have to be tested to have (beta)(0.15) = 0.10 for the test in part (a)?