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3. Brunt, Rhee, and Zhong (2008) surveyed 557 under- graduate college students to examine their weight status, health behaviors, and diet. Using body mass index (BMI), they classified the students into four categories: underweight, healthy weight, overweight, and obese. They also measured dietary variety by counting the number of different foods each student ate from several food groups. Note that the researchers are not measuring the amount of food eaten, but rather the number of different foods eaten (variety, not quantity). Nonetheless, it was somewhat surprising that the results showed no differences among the four weight categories that were related to eating fatty and/or sugary snacks.
Suppose a researcher conducting a follow up study obtains a sample of n = 25 students classified as healthy weight and a sample of n = 36 students clas- sified as overweight. Each student completes the food variety questionnaire, and the healthy-weight group produces a mean of M = 4.01 for the fatty, sugary snack category compared to a mean of M = 4.48 for the overweight group. The results from the Brunt, Rhee, and Zhong study showed an overall mean vari- ety score of µ = 4.22 for the discretionary sweets or fats food group. Assume that the distribution of scores is approximately normal with a standard deviation of (J = 0.60.
a. Does the sample of n = 36 indicate that number of fatty, sugary snacks eaten by overweight students is significantly different from the overall popula- tion mean? Use a two-tailed test with a = .05.
b. Based on the sample of n = 25 healthy-weight students, can you conclude that healthy-weight students eat significantly fewer fatty, sugary snacks than the overall population? Use a one- tailed test with a = .05.