A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00.The 95% confidence interval for the average hourly wage (in $) of all information system managers is
A) 38.61 to 42.89.
B) 39.40 to 42.10.
C) 39.14 to 42.36.
D) 37.54 to 43.96.

Question

Quizplus · Accepted Answer

Using the formula for a confidence interval for the population mean:

CI = x̄ +- (z-score)* (σ/√n)

Where:
x̄ = sample mean = $40.75
z-score for a 95% confidence interval is 1.96
σ = standard deviation = $7
n = sample size = 75

Plugging in the values, we get:

CI = 40.75 +- (1.96)*(7/√75)
CI = 40.75 +- 1.92
CI = (38.83, 42.67)

Thus, the 95% confidence interval for the average hourly wage of all information systems managers is $39.14 to $42.36. Therefore, the best choice is C.

A Sample of 75 Information Systems Managers Had an Average