The U.S. Department of Agriculture's National School Lunch Program mandates that for a high school to receive reimbursement for school lunches, the number of calories served at lunch must be no more than 850 calories. However, a nutritionist believes that the true mean number of calories served at lunch at her local high school exceeds 850 calories. Collaborating with the Food Department of the school district, she randomly selected 30 lunch menus for the local high school and recorded the number of calories served at lunch in each menu. She found that the mean number of calories for these 30 school lunches is 867 with a standard deviation of 65.8.
Carry out a hypothesis test at the level of α=0.05, following the steps below, to test the nutritionist's claim that the school lunches at her local high school have more calories than the national average of 850 calories. Show your formula set up or your calculator command.
(2 pts) Find the test statistic. Show your formula set up or calculator command.
(1) Find the critical value OR the P-value of the test.
(2) State the statistical decision of the test and justify your conclusion.
(3) Interpret your decision in the context of the problem. Use full sentences.