the Wall Street Journal reported that automobile crashes cos

the Wall Street Journal reported that automobile crashes cost United States $162 billion annually. The average cost per person for crashes in the Tampa, Florida area was reported to be $1599. Suppose the average cost was based on a sample of 50 persons who had been involved in crashes and that the population standard deviation is $600.

a.) What is the margin of error for a 95% confidence interval?

b.) what would you recommend if the study required a margin of error of $150 or less?

Solution

a)

As

E = z*sigma / sqrt(n)

and for a 95% confidence interval,

z = 1.959963985

Then, as sigma = 600, n = 50,

E = 166.3084589 [answer]

b)

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    600  
E = margin of error =    150  
      
Thus,      
      
n =    61.46334113  
      
Rounding up,      
      
n =    62   [ANSWER]

We recommend to increase the sample size to 62.