Susan is in charge of quality control at a small fruit juice

Susan is in charge of quality control at a small fruit juice bottling plant. Each bottle produced is supposed to contain exactly 12 fluid ounces (fl oz) of juice. Susan decides to test this by randomly sampling 30 filled bottles and carefully measuring the amount of juice inside each. She will recalibrate the machinery if the average amount of juice per bottle differs from 12 fl oz at the 1 % significance level. The sample of 30 bottles has an average of 11.92 fl oz per bottle and a standard deviation of 0.26 fl oz. Find test statistic and p-value to the third decimal place.

Solution

The test statistic is

t=(xbar-mu)/(s/vn)

=(11.92-12)/(0.26/sqrt(30))

=-1.685

The degree of freedom =n-1=30-1=29

It is a two-tailed test.

So the p-value= 2*P(t with df=29<-1.685) =0.103 (from student t table)