6414 A study was conducted to estimate hospital costs for ac

6.4.14 A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution that appears to be bell-shaped with a mean of $9004 with a standard deviation of $5629. a1) Construct the 99% confidence interval for the mean of all such costs. b) If you are a manager for an insurance company that for drivers who wear seat belts, and you want conservative case scenario, what amount should you use as the possible accident victim who wears seat belts? of all such costs.

Solution

a)

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    9004          
t(alpha/2) = critical t for the confidence interval =    2.860934606          
s = sample standard deviation =    5629          
n = sample size =    20          
df = n - 1 =    19          
Thus,              
Margin of Error E =    3601.008794          
Lower bound =    5402.991206          
Upper bound =    12605.00879          
              
Thus, the confidence interval is              
              
(   5402.991206   ,   12605.00879   ) [ANSWER]

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b)

We use the upper bound, $12605.01, because that would be the worst case scenatio if you are a manager.