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Chapter 3: Q 3. (page 171)

Heavy backpacks Ninth-grade students at the Webb Schools go on a

backpacking trip each fall. Students are divided into hiking groups of size 8 by selecting names from a hat. Before leaving, students and their backpacks are weighed. The data here are from one hiking group. Make a scatterplot by hand that shows how to backpack weight relates to body weight.

Short Answer

Expert verified

There is a positive relationship between the two variables.

Step by step solution

01

Given information

The data set is:

Body weight120187109103131165158116
Backpack weight2630262429353128
02

Explanation

The scatter plot for the provided set can be constructed as:

The above-drawn graph demonstrates that the two variables have a positive association.

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Most popular questions from this chapter

Olympic athletes The scatterplot shows the relationship between height (in

inches) and weight (in pounds) for the members of the United States 2016 Olympic Track and Field team.10 Describe the relationship between height and weight for these athletes.

Do muscles burn energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate of 12 women who are subjects in a study on dieting. Lean body mass, given in kilograms, is a person’s weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours. The researchers believe that lean body mass is an

important influence on metabolic rate.

a. Make a scatterplot to display the relationship between lean body mass and metabolic rate.

b. Describe the relationship between lean body mass and metabolic rate.

The scatterplot shows the lean body mass and metabolic rate for a sample of = adults. For each person, the lean body mass is the subject’s total weight in kilograms less any weight due to fat. The metabolic rate is the number of calories burned in a 24-hour period.

Because a person with no lean body mass should burn no calories, it makes sense to model the relationship with a direct variation function in the form y = kx. Models were tried using different values of k (k = 25, k = 26, etc.) and the sum of squared residuals (SSR) was calculated for each value of k. Here is a scatterplot showing the relationship between SSR and k:

According to the scatterplot, what is the ideal value of k to use for predicting metabolic rate?

a. 24

b. 25

c. 29

d. 31

e. 36

A student wonders if tall women tend to date taller men than do short

women. She measures herself, her dormitory roommate, and the women in the adjoining dorm rooms. Then she measures the next man each woman dates. Here are the data (heights in inches):

a. Make a scatterplot of these data. Describe what you see.

b. Find the correlation r step by step, using the formula on page 166. Explain how your value for r matches your description in part (a).

An AP® Statistics student designs an experiment to see whether today’s high school students are becoming too calculator-dependent. She prepares two quizzes, both of which contain 40 questions that are best done using paper-and-pencil methods. A random sample of 30 students participates in the experiment. Each student takes both quizzes—one with a calculator and one without—in random order. To analyze the data, the student constructs a scatterplot that displays a linear association between the number of correct answers with and without a calculator for the 30 students. A least-squares

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Which of the following statements is/are true?

I. If the student had used Calculator as the explanatory variable, the correlation would remain the same.

II. If the student had used Calculator as the explanatory variable, the slope of the least-squares line would remain the same.

III. The standard deviation of the number of correct answers on the paper-and-pencil quizzes was smaller than the standard deviation on the calculator quizzes.

a. I only

b. II only

c. III only

d. I and III only

e. I, II, and III
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