Question

Suppose the management at a local health system must report the average annual income of their physicians. In order to do so, the health system conducts a SRS of 439 of their full-time physicians and calculates a sample average income of $134,257.00. The population standard deviation is assumed to be $18,437.00. Assume the health system must report their statistics with “virtual certainty” i.e. they must use a Z value of 3.0 in all statistical operations.

A) Construct a confidence interval for the annual income of the physicians employed by the health center with “virtual certainty”.

B) Interpret the interval calculated in the above response.

Answer 1

Answer

(A) given that

mean = 134257

standard deviation = 18437

sample size n = 439

z critical = 3

confidence interval =

(B) We are 95% confident that the true annual income of the physicians employed by the health center with virtual certainty is between $131617.15 and $136896.85