Refer to the Journal of Consumer Behaviour (Vol. 10, 2011) study of packaging of a children's health food product, Exercise 7.33. Recall that a fictitious brand of a healthy food product- sliced apples-was packaged to appeal to children. The researchers compared the appeal of this fictitious brand to the appeal of a commercially available brand of sliced apples, which was not packaged for children. Each of 408 schoolchildren rated both brands on a 5-point "willingness to eat" scale, with 1 = "not willing at all" and 5 = "very willing." The fictitious brand had a sample mean score of 3.69, while the commercially available brand had a sample mean score of 3.00. The researchers wanted to compare the population mean score for the fictitious brand, mF, with the population mean score for the commercially available brand, mC. They theorized that mF would be greater than mC.
a. Specify the null and alternative hypotheses for the test.
b. Explain how the researchers should analyze the data and why.
c. The researchers reported a test statistic value of 5.71. Interpret this result. Use a = .05 to make your conclusion.
d. Find the approximate p-value of the test.
e. Could the researchers have tested at a = .01 and arrived at the same conclusion?