Question

Ardith Brunt and coworkers surveyed 557 undergraduate 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 foa ach student ate from several food groups. Note that the researchers were not measuring the amount of food eate but rather the number of different foods eaten (variety, not quantity). Nonetheless, it was somewhat surprising tha the results showed no differences that were related to eating fatty and/or sugary snacks among the four weight categories. [Brunt, A., Rhee, Y., & Zhong, L. (2008). Differences in dietary patterns among college students accord to body mass index. Journal of American College Health, 56, 629-634.] Suppose a researcher conducting a follow-up study obtains a sample of n = 25 students classified as being of healt weight and a sample of n 36 students classified as overweight. Each student completes the food variety questionnaire, and the healthy-weight group produces a mean of M = 3.95 for the fatty/sugary snack category, compared to a mean of M = 4.41 for the overweight group. The results from the Brunt et al. study showed an over mean variety score of μ = 4.22 for the fatty/sugary snack food group. Assume that the distribution of scores is approximately normal with a standard deviation of ơ-0.60 Does the sample of n 36 indicate that the number of fatty/sugary snacks eaten by overweight students is significantly different from the overall population mean? Use a two-tailed test with α = .05. A Standard Normal Distribution tool is available at the end of this problem. Use two decimal places for z scores and critical values For this sample, z -1.90 and the critical value for z is 2.58 The number of fatty/sugary snacks eaten overweight students is significantly different from the number eaten by the general population Based on the sample of n 25 healthy-weight students, can the researcher conclude that healthy-weight students at significantly fewer fatty/sugary snacks than the overall population? Use a one-tailed test with a-.05 eat For this sample z2.70 and the critical value for z is -2.33.Healthy-weight students do significantly fewer fatty/sugary snacks than the general population does

Answer 1

For overweight students, 2 tailed at $\alpha$ = 0.05, n= 36

z = (4.41-4.22)/[0.6/sqrt(36)] = 1.9

The critical values are $\pm$ 1.96

Since 1.9 lies in between -1.96 and 1.96, the number of fatty/sugary snacks eaten by overweight students is not significantly different from the number eaten by the general population.

For healthy weight students, 1 tailed at $\alpha$ = 0.05, n = 25

z = (3.95-4.22)/[0.6/sqrt(36)] = -2.7

The critical values are -1.645

Since t_test(-1.645) is > t_critical(-2.7), Healthy weight students do not eat significantly fewer fatty/sugary snacks than the general population does.