A machine that is programmed to package 1.20 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and the standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively.

1. Set up the null and the alternative hypotheses to determine if the machine is working improperly-that is, it is either underfilling or overfilling the cereal boxes.
2. Calculate the value of the test statistic and the p-value.
3. At the 5% level of significance, can you conclude that the machine is working improperly? Explain.