Question

It is suspected that there are problems with laminate plates manufactured by a certain plant. In

particular, it appears that the deviation of the actual thickness from the target value of 5mm is

unacceptably high. To make a decision whether the plant needs to be reviewed, 25 plates are

randomly selected and their thicknesses are measured. If the corresponding sample standard

deviation exceeds 0.25 mm, a plant review is recommended. The measurements were carried

out, and a particular sample of 25 plates produced the sample standard deviation of 0.21 mm.

What is the (approximate) probability of observing a sample standard deviation of 0.21 mm

(or less) even though the true standard deviation of the plate thickness is 0.29 mm? In other

words, what is the probability that the sample analyzed only consisted of ‘good’ plates with

acceptable deviations (and it was, therefore, concluded that there is nothing wrong with the

plant) when, in fact, the true standard deviation is unacceptably high and the revision is needed?

This scenario is somewhat the opposite of the one discussed in question 1, where we were

talking about mistakenly reviewing the production line that is perfectly fine. （Answer 0.025）

Answer 1

[ The above probability is obtained from the chi-square table and also from the Excel 07 function =1-CHIDIST(24*0.21^2/0.0841,24) . ]