Suppose approximately 900 people die in bicycle accidents each year. One study e

Question

Suppose approximately 900 people die in bicycle accidents each year. One study examined the records of 1911 bicyclists aged 15 or older who were fatally injured in bicycle accidents in a five-year period and were tested for alcohol. Of these, 442 tested positive for alcohol (blood alcohol concentration of 0.01% or higher).

(b) To do statistical inference for these data, we think in terms of a model where p is a parameter that represents the probability that a tested bicycle rider is positive for alcohol. Find a 99% confidence interval for p. (Round your answers to four decimal places.)

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(c) Can you conclude from your analysis of this study that alcohol causes fatal bicycle accidents? Explain.

Yes, we know that of the 900 people that die in bicycle accidents each year, about 442 test positive for alcohol.No, we do not know, for example, what percentage of cyclists who were not involved in fatal accidents had alcohol in their systems.    

(d) In this study 390 bicyclists had blood alcohol levels above 0.10%, a level defining legally drunk at the time. Give a 99% confidence interval for the proportion who were legally drunk according to this criterion. (Round your answers to four decimal places.)

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Explanation / Answer

b.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=442
Sample Size(n)=1911
Sample proportion = x/n =0.231
Confidence Interval = [ 0.231 ±Z a/2 ( Sqrt ( 0.231*0.769) /1911)]
= [ 0.231 - 2.576* Sqrt(0) , 0.231 + 2.58* Sqrt(0) ]
= [ 0.2065,0.2561]
c.
No, we do not know, for example, what percentage of cyclists who were not
involved in fatal accidents had alcohol in their systems.
d.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=390
Sample Size(n)=1911
Sample proportion = x/n =0.204
Confidence Interval = [ 0.204 ±Z a/2 ( Sqrt ( 0.204*0.796) /1911)]
= [ 0.204 - 2.576* Sqrt(0) , 0.204 + 2.58* Sqrt(0) ]
= [ 0.1803,0.2279]

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