Apia: Student Question e MindTap . Cengage Lear: :× × Ye Chogg Study order Conf

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Apia: Student Question e MindTap . Cengage Lear: :× × Ye Chogg Study order Conf I https://courses.aplia.com/af/serviet/quiz?quiz action-takeQuiz&quiz; probGuid QNAPCOA80101000000414d8c40060000&ctx-cansorge-0057;&ck; m 153015 × 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 each 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, 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 u 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 t from the overall population mean? Use a two-tailed test with a .05. A Standard Normal Distribution tool is available at the end of this problem. Use two decimal places for z scores and critical values. The number of fatty/sugary snacks eaten by For this sample, z overweight students , and the critical value for z 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 eat significantly fewer fatty/sugary snacks than the overall population? Use a one-tailed test with a os. eat , and the critical value for z is Healthy-weight students For this sample z significantly fewer fatty/sugary snacks than the general population does.

Explanation / Answer

Here we have give two groups one is healthy student and other one is overweight student.

a) Now we have to test the hypothesis that,

H0 : mu = 4.22 Vs H1 : mu not= 4.22

where mu is population mean for overweight student.

Assume alpha = level of significance = 0.05

Given that,

For 5% level of significance critical value = -1.96 and 1.96

The test statistic is,

Z = (Xbar - mu) / (sigma / sqrt(n))

= (4.41 - 4.22) / (0.6/sqrt(36))

= 1.9

Here Z < critical value

Accept H0 at 5% level of significance.

COnclusion : There is not sufficient evidence to say that the number of fatty / sugary snacks eaten by overweight students is significantly different from overall population mean.

b) Here we have to test the hypothesis that,

H0 : mu = 4.22 Vs H1 : mu < 4.22

where mu is population mean for healthy students.

Assume alpha = level of significance = 0.05

Given that,

Test statistic is,

Z = (Xbar - mu) / (sigma / sqrt(n)) = (3.95 - 4.22) / (0.6 / sqrt(25)) = -2.25

And for 0.05 level of significance critical value = -1.96

Test statistic > critical value

Reject H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that healthy weight students are significantly fewer fatty/ sugary snacks than the geneal population does.

overweight n2 36 m2 4.41 mu 4.22 sigma 0.6

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