Question

A random sample of 8 recent college graduates found that starting salaries for computer scientists had a mean of $85000 and a standard deviation of $15000. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all computer scientists in gainesville.

Answer 1

Answer:

(72460, 97540)

Step-by-step explanation:

Given:-

- The sample size, n = 8

- The sample parameters of normal distributed data:

                     mean u = $85000

                     standard deviation s.d = $15000

Find:-

Construct a 95% confidence interval for the average starting salary of all computer scientists in gainesville.

Solution:-

- A random variable (X) denotes average starting salary of all computer scientists in gainesville has a sample normally distribution as follows:

                              X ~ N ( $85000 , $15000^2 )

- The general formulation for CI for known standard deviation with significance α = 1 - 0.95 = 0.05:

                    ( u - Z_a/2*(s.d/√n) < X < u + Z_a/2*(s.d/√n) )

- The Z_a/2 = Z_0.025 = 1.96:

                    ( 85,000 - 1.96*(15,000/√8) < X < 85,000 + 1.96*(15,000/√8) )

                    (72460, 97540)