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
 = 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
 = 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;
 is;
P(-1.672 <  < 1.672) = 0.90  {As the critical value of t at 59 degrees of
 < 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
 < 1.672) = 0.90
P(  <
 <  <
 <  ) = 0.90
 ) = 0.90
P(  <
 <  <
 <  ) = 0.90
 ) = 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]
.