A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively.
a. Set up the null and the alternative hypotheses to determine if the machine is working improperly, that is, it is either under-filling or over-filling the cereal boxes.
b. Calculate the value of the test statistic.
c. Approximate the p-value. At a 5% level of significance, can you conclude that the machine is working improperly? Explain.
d. Repeat the exercise using the critical value approach.