Elementary Statistics: Picturing the World (7th Edition)

7th Edition

ISBN: 9780134683416

Author: Ron Larson, Betsy Farber

Publisher: PEARSON

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Textbook Question

Chapter 8.2, Problem 3CS

How Protein Affects Weight Gain in Overeaters

In a study published in the Journal of the American Medical Association, three groups of 18- to 35-year-old participants overate for an 8-week period. The groups consumed different levels of protein in their diet. The low protein group's diet was 5% protein, the normal protein group’s diet was 15% protein, and the high protein group’s diet was 25% protein. The study found that the low protein group gained considerably less weight than the normal protein group or the high protein group.

You are a scientist working at a health research firm. The firm wants you to replicate the experiment. You conduct a similar experiment over an 8-week period. The results of the experiment are shown below.

Chapter 8.2, Problem 3CS, How Protein Affects Weight Gain in Overeaters In a study published in the Journal of the American

EXERCISES

In Exercises 1–3, perform a two-sample t-test to determine whether the mean weight gains of the two indicated studies are different. Assume the populations are normally distributed and the population variances are equal. For each exercise, write your conclusions as a sentence. Use α = 0.05.

3. Test the weight gains of the normal protein group against those in the high protein group.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter 8.2, Problem 2CS

Chapter 8.2, Problem 4CS

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Do people feel hungrier after sampling a healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was described as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). Treatment Group Healthy Tasty 5 8 7 Hunger Rating No Snack 3 4 4 4 1 4 2 7 3 6 2 5 6 5 5 4 7 5 2 3 4 6 4 4 Sample Mean 5.6667 3.4444 4.2222 Sample…

Do people feel hungrier after sampling a healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was described as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). TreatmentGroup Hunger Rating SampleMean SampleStandardDeviation Healthy 5 8 7 4 7 3 4 7 6 5.6667 1.7321 Tasty 4 1 5 2 6 2 5 3 4 3.5556…

Do people feel hungrier after sampling a healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was billed as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). Treatment Group Hunger Rating Sample Mean Sample Standard Deviation Healthy 5 7 7 4 7 3 4 7 6 5.6 1.59 Tasty 4 1 5 2 6 2 5 3 4 3.6 1.67 No Snack 3 4 5…

Chapter 8 Solutions

Elementary Statistics: Picturing the World (7th Edition)

Ch. 8.1 - Classify each pair of samples as independent or...Ch. 8.1 - A survey indicates that the mean annual wages for...Ch. 8.1 - A travel agency claims that the average daily cost...Ch. 8.1 - What is the difference between two samples that...Ch. 8.1 - Explain how to perform a two-sample z-test for the...Ch. 8.1 - Describe another way you can perform a hypothesis...Ch. 8.1 - What conditions are necessary in order to use the...Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Independent and Dependent Samples In Exercises 58,...

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Solution Summary: The author identifies the claim and states that there is significant difference in the mean weight gains of the normal and high protein groups.

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