A jar filling process is known to have an associated standar

A jar filling process is known to have an associated standard deviation of = 1.6g net weight. Suppose that with a declared (label) weight on each jar of 135g, process engineers have set a target mean net weight at 135 + 3 = 139.8g. Suppose further that in a routine check of filling process performance, intended to detect any changes of the process mean from its target value, a sample of n = 25 jars produced a sample mean fill weight of 139.0g.

a) What does this value of ¯x have to say about the plausibility of the current process mean actually being at the target mean of 139.8g? Is there evidence that we are at less than the target mean? Use a formal testing procedure with a significance level of 0.05.

b) Quality control, which is reflected by the variance, is also of concern. Compute the probability that the sample standard deviation exceeds 1.3

Solution