Suppose approximately 900 people die in bicycle accidents each year. One study e
ID: 3174947 • Letter: S
Question
Suppose approximately 900 people die in bicycle accidents each year. One study examined the records of 1711 bicyclists aged 15 or older who were fatally injured in bicycle accidents in a five-year period and were tested for alcohol. Of these, 642tested positive for alcohol (blood alcohol concentration of 0.01% or higher).
(a) Summarize the data with appropriate descriptive statistics. (Round your answer to four decimal places.)
p =
(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.)
,
(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 642 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 592 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.)
,
Explanation / Answer
a. The sample proportion, phat=x/n, where, x denotes number of events with specific characteristic, and n denotes number of trials.
phat=642/1711
=0.3752 (ans)
b. The 99% c.i for true population proportion of bicycle riders who were tested positive for alcohol is as follows:
phat+-zsqrt[phat(1-phat)/n], where, phat is sample proportion, z denotes z critical at alpha/2, and n is sample size.
=0.3752+-2.576 sqrt[0.3752(1-0.3752)/1711]
=0.3452, 0.4060
c. The interval doesnot contain hypothesized value of the parameter, therefore, reject null hypothesis, H0: p=0.5 and conclude that alcohol causes fatal bicycle accidents.
d. The 99% c.i=phat+-zsqrt[phat(1-phat)/n]
=592/1711+-2.576 sqrt[592/1711(1-592/1711)/1711]
=0.3165, 0.3763 (ans)
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