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

X_bar = 47505

n= 33

= 1535

Now calculate 95% of confidence with formula

CI = x_bar z*(/n)

Therefore z value for 95% confidence interval is 1.96.

z = 1.96

CI = 47505 1.96 *(1535/33)

= 47505 523.73

CI = 47505 - 523.73 and CI = 47505 + 523.73

= 46981.27 and CI = 48028.73

Therefore 95% confidence interval is

(46981.27, 48028.73)

Interpretation:

We are 95% confident that the interval from 46981.27 to 48028.73 actually does contain the true value of the population parameter.