Question

Last year's records of auto accidents occurring on a given section of highway were classified according to whether the resulting damage was $1,000 or more and to whether a physical injury resulted from the accident. The data follows.

	Under $1,000	$1,000 or More
Number of Accidents	39	40
Number Involving Injuries	10	23

(a) Estimate the true proportion of accidents involving injuries when the damage was $1,000 or more for similar sections of highway. (Round your answer to three decimal places.)


Find the 95% margin of error. (Round your answer to three decimal places.)


(b) Estimate the true difference in the proportion of accidents involving injuries for accidents with damage under $1,000 and those with damage of $1,000 or more. Use a 95% confidence interval. (Use p₁ − p₂ where p₁ is the proportion of accidents involving injuries with damage under $1,000 and p₂ is the proportion of accidents involving injuries with damage of $1,000 or more. Round your answers to three decimal places.)

Answer 1

Given,

	Under $1,000	$1,000 or More
Number of Accidents	39	40
Number Involving Injuries	10	23

(a)

Estimate for true proprotion of accidents in involving injuries when the damage was $1,000 or more for similar sections of highway = Sample proportion of accidents in involving injuries when the damage was $1,000 or more for similar sections of highway  

: Sample proportion of accidents in involving injuries when the damage was $1,000 or more for similar sections of highway =x: Number of accidents Involving Injuries when the damage was $1,000 or more for similar sections of highway/ n: Total number of accidents when the damage was $1,000 or more for similar sections of highway =40/23= 0.575

Estimate for true proprotion of accidents in involving injuries when the damage was $1,000 or more for similar sections of highway = 0.575

Formula for 95% Margin of error for true proportion:

Given
n : Sample Size	40
x	23
: Sample Propotion of Sample : x/n	0.575
Confidence Level	95%
(= 100-95/100=5/100 ) = 0.05	0.05
/2 (=0.05/2=0.025)	0.025
	1.96

95% margin of error:

95% Margin of error for true proportion: 0.153198

(b)

	Under $1,000	$1,000 or More
Number of Accidents n	39	40
Number Involving Injuries:x	10	23
SampleProportion of accidents involving in injuries	=10/39=0.2564	=23/40=0.575

: Sample proportion of accidents in involving injuries when the damage was $1,000 or more for similar sections of highway =x₁: Number of accidents Involving Injuries when the damage was $1,000 or more for similar sections of highway/ n₁: Total number of accidents when the damage was $1,000 or more for similar sections of highway =23/40= 0.575

: Sample proportion of accidents in involving injuries when the damage was under $1,000 for similar sections of highway =x: Number of accidents Involving Injuries when the damage was $1,000 or more for similar sections of highway/ n: Total number of accidents when the damage was under $1,000 for similar sections of highway =10/39= 0.2564

Estimate the true difference in the proportion of accidents involving injuries for accidents with damage under $1,000 and those with damage of $1,000 or more = = 0.2564-0.575=-0.3186

Formula for confidence interval for difference of two population proportions : p1-p2

:	0.2564
	0.575
Confidence Level	95%
(= 100-95/100=5/100 ) = 0.05	0.05
/2 (=0.05/2=0.025)	0.025
	1.96

95% Confidence Interval for Difference in two Population proportions

95% confidence intervale estimate for true difference in the proportion of accidents involving injuries for accidents with damage under $1,000 and those with damage of $1,000 or more =(-0.5241,-0.1131)