Suppose approximately 900 people die in bicycle accidents ea

Suppose approximately 900 people die in bicycle accidents each year. One study examined the records of 1611 bicyclists aged 15 or older who were fatally injured in bicycle accidents in a five-year period and were tested for alcohol. Of these, 542 tested positive for alcohol (blood alcohol concentration of 0.01% or higher). Summarize the data with appropriate descriptive statistics. (Round your answer to four decimal places.) 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.) 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 542 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. In this study 492 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.)

Solution

a)
tested Positive(x)=542
Sample Size(n)=1611
Sample proportion = x/n =0.3364
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

Confidence Interval = [ 0.3364 ±Z a/2 ( Sqrt ( 0.3364*0.6636) /1611)]
= [ 0.3364 - 2.58* Sqrt(0.0001) , 0.3364 + 2.58* Sqrt(0.0001) ]
= [ 0.306,0.3668]

c)
No, we don\'t know for example what percentage of cyclists who were not involved in    fata accidents had alcohal in their systems

d)

Bicyclists had blodd alocohals above 0.10%(x)=492
Sample Size(n)=1611
Sample proportion = x/n =0.3054
Confidence Interval = [ 0.3054 ±Z a/2 ( Sqrt ( 0.3054*0.6946) /1611)]
= [ 0.3054 - 2.58* Sqrt(0.0001) , 0.3054 + 2.58* Sqrt(0.0001) ]
= [ 0.2758,0.335]