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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Brunt, Rhee, and Zhong (2008) 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 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 tour 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 classified 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 variety 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 σ = 0.60.

  1. a. Does the sample of n = 36 indicate that the number of fatty, sugary snacks eaten by overweight students is significantly different front the overall population mean? Use a two-tailed test with α = .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 α = .05.

a.

To determine
 Whether the number of fatty, sugary snacks eaten by overweight students is significantly different from the overall population mean with α=0.05

Explanation

Given info:

The sample size n=36, sample mean M=4.48, population mean μ=4.22 standard deviation σ=0.60 and level of significance α=0.05.

Calculation:

The test hypotheses are;

Null hypothesis:

H0:μ=4.22

That is, the mean variety score is 4.22.

Alternate hypothesis:

H1:μ4.22

That is, the mean variety score is different from 4

b.

To determine
 Whether the healthy snacks taken by the students is significantly less than the overall population mean with α=0.05

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