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.
State the null and alternative hypotheses.
Give the test statistic and the -value and state the conclusion of the test.
Should Susan recalibrate the machinery?