Question

The rising cost of malpractice insurance is a growing problem. A random sample of thirty-three General Surgery claims from TN had a mean cost of $47505 with a standard deviation of $1535.

a.     Find a 95% confidence interval for the mean claim amount of all General Surgery claims in TN.

b.     Interpret the confidence interval in the words of the problem.

c.      Find the error bound.

d.     A senator claims that mean for all General Surgery claims in TN is more than $45000. Is there evidence to support or refute this claim? Justify!

Answer 1

given data are :-

sample mean () = 47505

sample sd (s) = 1535

sample size (n ) = 33

a). df = (n-1) = (33-1) = 32

t critical value for 95% confidence level, both tailed test be:-

[ using t distribution table, for df = 32, alpha= 0.05 , both tailed test]

the 95% confidence interval for the mean claim amount of all General Surgery claims in TN is:-

b).interpretation:-

we are 95% confident that the mean for all General Surgery claims in TN will be within $46961 and $ 48049.

c).the error bound is:-

d).yes, there is sufficient evidence to support the claim that mean for all General Surgery claims in TN is more than $45000.

because all the values (upper limit and lower limit) of the 95% confidence interval is greater than 45000.