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Last year\'s records of auto accidents occurring on a given section of highway w

ID: 3062904 • Letter: L

Question

Last year's records of auto accidents occurring on a given section of highway were classified according to whether the resulting damage was $1000 or more and to whether a physical injury resulted from the accident. The data follows. Under $1000 $1000 or More Number of Accidents 36 43 Number Involving Injuries 10 23 (a) Estimate the true proportion of accidents involving injuries when the damage was $1000 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 $1000 and those with damage of $1000 or more. Use a 95% confidence interval. (Round your answers to three decimal places.) to

Explanation / Answer

Solution:-

a) p = 23/43 = 0.535

95% of the marign of error , Z = 1.96

ME = Z *sqrt(p*q/n) = 1.96*sqrt(0.535*0.465/43) = 0.149

b) p1 = 10/36 =  0.278 , q1 = 0.722

p2 = 23/43 = 0.535 , q2 =  0.465

95% confidence interval true difference : (p1-p2) +/-( Z*(sqrt((p1q1/n1)+(p2q2/n2)))

: (0.278 - 0.535) +/- (1.96*(sqrt(0.278*0.722/36)+(0.535*0.465/43)))

: -0.415 , -0.099

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