Answer:
A 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .
Step-by-step explanation:
We are given that a researcher randomly selects records from 60 such drivers in 2009 and determines the sample mean BAC to be 0.16 g/dL with a standard deviation of 0.080 g/dL.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~
where, = sample mean BAC = 0.16 g/dL
s = sample standard deviation = 0.080 g/dL
n = sample of drivers = 60
= population mean BAC in fatal crashes
<em>Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation. </em>
So, a 90% confidence interval for the population mean, is;
P(-1.672 < < 1.672) = 0.90 {As the critical value of t at 59 degrees of
freedom are -1.672 & 1.672 with P = 5%} P(-1.672 < < 1.672) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u>90% confidence interval for</u> = [
,
]
= [ ,
]
= [0.143, 0.177]
Therefore, a 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .