Problem 33E

Packaging of a children’s health food. Junk foods (e.g., potato chips) are typically packaged to appeal to children. Can similar 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: 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

a. Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded 3. Use 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.

Answer

Step 1 of 2

(a)

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.”

We have given a sample of 408 school children.

Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is

We are asked to conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded

Use to make your conclusion.

Let be the true mean willingness to eat the brand of sliced apples.

To determine if the true mean willingness to eat the brand of sliced apples exceeds 3, we test the following hypothesis,

We can write,

An upper or right tailed test about a population mean is,

Figure 1: One Proportion (upper tail test)

Rejection rule for an upper tail test: The Critical Value Approach from the figure 1

……..(1)

Hence the test statistic for hypothesis tests about a population mean when is known,

………(2)

We know hence we can rewrite the equation (2),

………(3)

The rejection region requires in the upper tail of the

From the table II, Appendix D, the value of

…….(4)

From equation (3) and (4) we can see that the observed value of the test statistic falls in the rejection region.

Since,

Hence is rejected and there is sufficient evidence to indicate that the true mean willingness to eat the brand of sliced apples exceeds 3 at