Lesson 4

Linear Models

Problem 1

The scatter plot shows the number of times a player came to bat and the number of hits they had.

A scatter plot. Horizontal, 0 to 600, by 50’s, labeled at bats. Vertical, 0 to 150, by 12 point 5’s, labeled hits. 19 dots trend linearly up and to the right.

The scatter plot includes a point at \((318,80)\). Describe the meaning of this point in this situation.

Solution

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Problem 2

The scatter plot shows the number of minutes people had to wait for service at a restaurant and the number of staff available at the time.

A scatter plot. Horizontal, 0 to 9, by point 5’s, labeled staff. Vertical, 0 to 13, by point 5’s, labeled wait time. 10 dots trend linearly down and to the right.

A line that models the data is given by the equation \(y = \text{-}1.62 x + 18\), where \(y\) represents the wait time, and \(x\) represents the number of staff available.

  1. The slope of the line is -1.62. What does this mean in this situation? Is it realistic?
  2. The \(y\)-intercept is \((0,18)\). What does this mean in this situation? Is it realistic?

Solution

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Problem 3

A taxi driver records the time required to complete various trips and the distance for each trip.

A scatter plot. Horizontal, 0 to 80, by 5’s, labeled time in minutes. Vertical, 0 to 40, by 5’s, labeled distance in miles. 14 dots trend linearly up and to the right with a line a best fit.

The best fit line is given by the equation \(y = 0.467x + 0.417\), where \(y\) represents the distance in miles, and \(x\) represents the time for the trip in minutes.

  1. Use the best fit line to estimate the distance for a trip that takes 20 minutes. Show your reasoning.
  2. Use the best fit line to estimate the time for a trip that is 6 miles long. Show your reasoning.

Solution

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Problem 4

Data is collected about the number of wins and losses by a random sample of teams with an animal mascot and those with another kind of mascot. The column relative frequencies are shown in the table. Based on the information in the table, is there an association between the variables? Explain your reasoning.

  animal mascot other type of mascot
wins 74% 49%
losses 26% 51%

 

Solution

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(From Unit 3, Lesson 3.)

Problem 5

A random selection of indoor and outdoor pool managers are surveyed about the number of people in each age group that swim there. Results from the survey are displayed in the two-way table. Based on the data, does there appear to be an association between pool type and age group? Explain your reasoning. 

  outdoor pool indoor pool
younger than 18 317 41
18 or older 352 163

 

Solution

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(From Unit 3, Lesson 3.)

Problem 6

Data from a random sample of people are collected about how they watch movies in the genres of action or mystery. Which value would best fit in the missing cell to suggest there is no association between the genre and how the movies are watched? 

  streaming movies disc rental
action 526 147
mystery 317  

 

A:

19

B:

89

C:

147

D:

320

Solution

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(From Unit 3, Lesson 3.)