A machine that is programmed to package $3\mathrm{.}00$ pounds of cereal in each cereal box is being tested for its accuracy. In a sample of $49$ cereal boxes the mean and the standars deviation are calculated as $3\mathrm{.}05$ and $0\mathrm{.}14$ pound respectively.

A$.$ Specify 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.

B$-1.$ Calculate the value of the test statistic

B$-2$ find the p value

C$-1$ what is the conclusion at $5\%$ significance level?

C$-2$ cab you conclude that the machine is not working properly