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.

(72460, 97540)

Step-by-step explanation:

Given:-

- The sample size, n = 8

- The sample parameters of normal distributed dа ta:

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)