Over the past 40 years, the percentage of homes in the United States with smoke detectors has risen steadily and has plateaued at about 96% as of 2015.† With this increase in the use of home smoke detectors, what has happened to the death rate from home fires? Suppose the following contains 17 years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million of population. Percentage of Homes with Smoke Detectors Home Fire Deaths per Million of Population 0.52 22.8 0.69 20.7 0.76 17.2 0.78 20.4 0.79 19.3 0.84 18.8 0.83 17.5 0.87 16.1 0.88 13.5 0.90 14.3 0.92 14.2 0.94 12.9 0.95 10.8 0.96 10.8 0.97 10.1 0.96 8.3 0.96 8.0 (a) Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Why or why not? We would expect there would be a ---Select--- negative positive relationship between smoke detector use and deaths from home fires. As more households have smoke detectors, warning of a fire would help the inhabitants of the home escape and lead to ---Select--- fewer more deaths from home fires. (b) Compute and report the correlation coefficient. (Round your answer to four decimal places.) Is there a positive or negative correlation between smoke detector use and deaths from home fires? Comment. There is ---Select--- a strong positive no a strong negative correlation between smoke detecter use and death from home fires. (c) Show a scatter plot of the death rate per million of population and the percentage of homes with smoke detectors. A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. A pattern goes down and right becoming more steep from (0.22, 22.8) to (0.67, 8). The points are scattered moderately from the pattern. A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. A pattern goes down and right becoming more steep from (0.52, 22.8) to (0.97, 8). The points are scattered moderately from the pattern. A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. A pattern goes up and right becoming more steep from (0.52, 8) to (0.97, 22.8). From left to right the points start close to the pattern, then become scattered widely from the pattern. A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. The points are scattered from 0.21 to 0.9 on the horizontal axis centered at 0.55 and from 12 to 20 on the vertical axis centered at 17.1. The points are scattered widely.

Over the past 40 years, the percentage of homes in the United States with smoke detectors has risen steadily and has plateaued at about 96% as of 2015.† With this increase in the use of home smoke detectors, what has happened to the death rate from home fires? Suppose the following contains 17 years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million of population. Percentage of Homes with Smoke Detectors Home Fire Deaths per Million of Population 0.52 22.8 0.69 20.7 0.76 17.2 0.78 20.4 0.79 19.3 0.84 18.8 0.83 17.5 0.87 16.1 0.88 13.5 0.90 14.3 0.92 14.2 0.94 12.9 0.95 10.8 0.96 10.8 0.97 10.1 0.96 8.3 0.96 8.0 (a) Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Why or why not? We would expect there would be a ---Select--- negative positive relationship between smoke detector use and deaths from home fires. As more households have smoke detectors, warning of a fire would help the inhabitants of the home escape and lead to ---Select--- fewer more deaths from home fires. (b) Compute and report the correlation coefficient. (Round your answer to four decimal places.) Is there a positive or negative correlation between smoke detector use and deaths from home fires? Comment. There is ---Select--- a strong positive no a strong negative correlation between smoke detecter use and death from home fires. (c) Show a scatter plot of the death rate per million of population and the percentage of homes with smoke detectors. A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. A pattern goes down and right becoming more steep from (0.22, 22.8) to (0.67, 8). The points are scattered moderately from the pattern. A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. A pattern goes down and right becoming more steep from (0.52, 22.8) to (0.97, 8). The points are scattered moderately from the pattern. A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. A pattern goes up and right becoming more steep from (0.52, 8) to (0.97, 22.8). From left to right the points start close to the pattern, then become scattered widely from the pattern. A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. The points are scattered from 0.21 to 0.9 on the horizontal axis centered at 0.55 and from 12 to 20 on the vertical axis centered at 17.1. The points are scattered widely.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 23PPS

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Question

Percentage of Homes with Smoke Detectors	Home Fire Deaths per Million of Population
0.52	22.8
0.69	20.7
0.76	17.2
0.78	20.4
0.79	19.3
0.84	18.8
0.83	17.5
0.87	16.1
0.88	13.5
0.90	14.3
0.92	14.2
0.94	12.9
0.95	10.8
0.96	10.8
0.97	10.1
0.96	8.3
0.96	8.0

(a)

Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Why or why not?

We would expect there would be a ---Select--- negative positive relationship between smoke detector use and deaths from home fires. As more households have smoke detectors, warning of a fire would help the inhabitants of the home escape and lead to ---Select--- fewer more deaths from home fires.

(b)

Compute and report the correlation coefficient. (Round your answer to four decimal places.)

Is there a positive or negative correlation between smoke detector use and deaths from home fires? Comment.

There is ---Select--- a strong positive no a strong negative correlation between smoke detecter use and death from home fires.

(c)

Show a scatter plot of the death rate per million of population and the percentage of homes with smoke detectors.

A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. A pattern goes down and right becoming more steep from (0.22, 22.8) to (0.67, 8). The points are scattered moderately from the pattern.

A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. A pattern goes down and right becoming more steep from (0.52, 22.8) to (0.97, 8). The points are scattered moderately from the pattern.

A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. A pattern goes up and right becoming more steep from (0.52, 8) to (0.97, 22.8). From left to right the points start close to the pattern, then become scattered widely from the pattern.

A graph has a horizontal axis labeled "Percentage of Homes with Smoke Detectors" with values from 0 to 1 and a vertical axis labeled "Home Fire Deaths per Million Population" with values from 0 to 25. The scatter diagram has 17 points. The points are scattered from 0.21 to 0.9 on the horizontal axis centered at 0.55 and from 12 to 20 on the vertical axis centered at 17.1. The points are scattered widely.

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