Can packaging of a healthy food product influence children's desire to consume the product? This was the question of interest in an article published in the Journal of Consumer Behaviour (Vol. 10, 2011). A fictitious brand of a healthy food product-sliced apples-was packaged to appeal to children (a smiling cartoon apple was on the front of the package). The researchers showed the packaging to a sample of 408 school children and asked each whether he or she was willing to eat the product. Willingness to eat was measured on a 5-point scale, with 1 = "not willing at all" and 5 = "very willing." The data are summarized as follows: x̅ = 3.69, s = 2.44. Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is μ = 3.

a. Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded 3. Use α = .05 to make your conclusion.

b. The data (willingness to eat values) are not normally distributed. How does this impact (if at all) the validity of your conclusion in part a? Explain.