Question: Recall the cost of food example from PS II. A study by the United States Department of Agriculture showed that the mean weekly cost to feed a family of four people on a moderate cost food plan was $156. A random sample of 100 families in the Pacific Northwest for followed a similar food plan had a sample mean cost of $164 with a sample standard deviation of $28. Does this data indicate that the population mean cost to feed a family of four on a moderate food plan is different in the Pacific Northwest than it is in the country as a whole?

(a) Calculate the observed significance level, the p-value. Compare the p-value to the \(\alpha \) -level and determine whether the null hypothesis should be rejected.

(b) Suppose you are asked to test the hypothesis that the mean is $156 versus the alternative hypothesis that the mean is greater than $156. Conduct the test at the \(\alpha \) = .05 level. Indicate the p-value here as well.

(c) Suppose that a sample of 25 families’ weekly food costs was collected and the sample mean was found to be $163 with a sample standard deviation of $25. Conduct a one-tailed test at an \(\alpha \) =.10 level that the true population mean is greater than $156.