Ardith Brunt and coworkers surveyed 557 undergraduate college students to examin

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 foods ach student ate from several food groups. Note that the researchers were 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 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 according 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 healthy 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 overall mean variety score of H 4.22 for the fatty/sugary snack food group. Assume that the distribution of scores is approximately normal with a standard deviation of -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 -,05. A Standard Normal Distribution tool is available at the end of this problem. Use two decimal places for z scores and critica For this sample, z overweight students , and the critical value for z is significantly different from th The number of fatty/sugary snacks eaten by #1.96 eaten by the general population 1 .65 +2.33 +1.65 s healthy-weight students, can tne rasearcher conclude that healthy-weight students Based on the sample of n "25 ca eat significantly fewer fatty/sugary snacks than the overall population? Use a one-tailed test with a os For this sample z significantly fewer fatty/sugary snacks than the general population does and the critical value for z is Healthy-weight students eat

Explanation / Answer

For overweight students
This is a two tailed test

mean = 4.22, x = 4.41 , n = 36 , s = 0.6

z = (x - mean) / (s/sqrt(n))
= ( 4.41 - 4.22) / ( 0.6 /sqrt(36))
= 1.9

The critical value for z is +/-1.96

The number of fatty snacks eaten by overweight students are not significantlly differnt than the general population

For healthy weight students
This is a one tailed test

mean = 4.22, x = 3.95 , n = 25 , s = 0.6

z = (x - mean) / (s/sqrt(n))
= ( 3.95 - 4.22) / ( 0.6 /sqrt(25))
= -2.25

The critical value for z is +1.65

Healthy weight students can eat significantlly fewer than the general population

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