A food company is developing a new granola bar, and its market analysts are curr

Question

A food company is developing a new granola bar, and its market analysts are currently working on preliminary studies of the packaging design. To help with a marketing strategy, the company was first interested in whether the appeal of the packaging design for the new product (and hence the appeal of the product itself) was related to a person’s gender. There were 100 male and 100 female volunteers available for purposes of evaluation. Both males and females rated the design on a scale of 1 to 10, 1 being “very unappealing” and 10 being “very appealing.” The mean rating for males was x1 = 7.4, with a standard deviation s1 = 1.5. The mean rating for females was x2 = 8.0, with a standard deviation s2 = 2.0. Let 1 and 2 represent the mean ratings we would observe for the populations of males and females, respectively, and assume our samples can be regarded as samples from these populations. Which of the following would lead us to believe that the t procedures were not safe to use here? a. The sample medians and means for the two groups were slightly different. b. The distributions of the data were moderately skewed. c. The data are integers between 1 and 10 and so cannot be normal. d. Only the most severe departures from normality would lead us to believe the t-procedures were not safe to use.

Explanation / Answer

OPTION c. The data are integers between 1 and 10 and so cannot be normal. [ANSWER]

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Note that normal distribution is continuous (can take on any value between an interval), but values here only take up integer values, so it cannot be normal.

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