A package of snack cakes claims that a single serving (one cake) has 160 calories. A consumer research group gathered a random sample of 40 cakes, which yielded a sample mean of 164 calories with a standard deviation of 18 calories. Is there evidence that the actual number of calories in these snack cakes is different from the 160 calories listed on the nutrition label? Test this hypothesis using a significance level of 5%.

a) What is the outcome variable? Is this outcome variable considered to be continuous or dichotomous?

b) Set up the appropriate null and alternative hypotheses for this study.

c) Select the appropriate test statistic. Should a z or t test statistic be used for this hypothesis test? Explain reasoning and/or show work.

d) Write out the decision rule for this hypothesis test. Make sure to include the appropriate z or t critical value.

e) Compute the appropriate test statistic for this hypothesis test. Show work.

f) Make a decision using the decision rule in (d) and the calculated test statistic in (e). Write out an appropriate conclusion.

g) Is it expected the p-value for this test to be greater than or less than the significance level of 0.05? Explain.