1. 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, we would expect that death rates due to home fires have decreased. The following table contains 17 years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million people: Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Percentage of Homes with Smoke Detectors 0.48 0.65 0.72 0.74 0.75 0.8 0.79 0.83 0.84 0.86 0.88 0.9 0.95 0.96 0.97 0.96 0.96 Home Fire Deaths per Million People 23 20.9 17.4 20.6 19.5 19 17.7 16.3 13.7 14.5 14.4 13.1 11 11 10.3 8.5 8.2 a. Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Explain. b. Draw a scatterplot of these data. You can do it either by hand or using Excel. c. Compute the covariance and 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 and relate to your scatterplot.

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1. 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, we would expect that death rates due to
home fires have decreased. The following table contains 17 years of data on the estimated
percentage of homes with smoke detectors and the estimated home fire deaths per million
people:
Year
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Percentage of
Homes with
Smoke
Detectors
0.48
0.65
0.72
0.74
0.75
0.8
0.79
0.83
0.84
0.86
0.88
0.9
0.95
0.96
0.97
0.96
0.96
Home Fire
Deaths per
Million People
23
20.9
17.4
20.6
19.5
19
17.7
16.3
13.7
14.5
14.4
13.1
11
11
10.3
8.5
8.2
a. Do you expect a positive or negative relationship between smoke detector use and
deaths from home fires? Explain.
b. Draw a scatterplot of these data. You can do it either by hand or using Excel.
c. Compute the covariance and 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 and relate to your scatterplot.
Transcribed Image Text:1. 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, we would expect that death rates due to home fires have decreased. The following table contains 17 years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million people: Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Percentage of Homes with Smoke Detectors 0.48 0.65 0.72 0.74 0.75 0.8 0.79 0.83 0.84 0.86 0.88 0.9 0.95 0.96 0.97 0.96 0.96 Home Fire Deaths per Million People 23 20.9 17.4 20.6 19.5 19 17.7 16.3 13.7 14.5 14.4 13.1 11 11 10.3 8.5 8.2 a. Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Explain. b. Draw a scatterplot of these data. You can do it either by hand or using Excel. c. Compute the covariance and 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 and relate to your scatterplot.
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