Question

E My Notes + Ask Your Teacher O 9. -/1 points ASWESBE9 3.E.059. 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 2015.1 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 astimated home fira deaths per millon of population. Home Fire Deaths per Million of Population Percentage of Homes with Smoke Detectors 0.51 22.8 0.68 20.7 0.75 17.2 0.77 20.4 0.78 19.3 0.83 18.8 0.82 17.5 0.86 16.1 0.87 13.5 0.89 14.3 0.91 14.2 0.93 12.9 0.95 10.8 0.96 10.8 0.97 10.1 0.96 8.3 0.95 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-- 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 -Selact-- deaths from home fires. (b) Compute and raport tha correlation coafficient. (Round your answer to four dacimal places.) Is there a positive or negative correlation between smoke detector use and deaths from home fires? Comment. Salect- Thera is 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. 25, 25 20 20 15 15 10- 10 0.8 0.2 0.4 0.6 0.2 0.4 0.6 0.8 Percentage of Homes with Percentage of Homes with Smoke Detectors Smoke Detectors 25 20 10 10 0.4 0.2 1.4 0.6 0.8 0.2 0.6 0.8 Percentage of Homes with Percentage of Homes with Smoke Detectors Smoke Detectors Need Help? Read it Talk to a Tutor Home Fire Deaths Home Fire Deaths er Million Population per Million Population Home Fire Deaths Home Fire Deuths per Million Population er Million Population

Answer 1

We would expect there would be a negative 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 decrease the number of deaths from home fires.

From the data given in the table, the calculated correlation coefficient between Percentage of Homes with Smoke detectors and Home fire deaths per million population is

-0.9098

The range of correlation coefficient is between -1 and +1,
-1 indicate perfect negative correlation and +1 indicate perfect positive correlation

Here the calculated value is very close to -1, indicates that the relationship is negative.

The scatter plot is

0.4 0.2 0.0 0.6 0.8 1.0 Percentage of Homes with Smoke Detectors Home Fire Deaths per Million Populaton 15