A sample of 100 information systems managers had an average hourly income of $40.00 with a standard deviation of $8.00. The 95% confidence interval for the average hourly wage (in $) of all information system managers is
A) 38.684 to 41.316.
B) 32 to 48.
C) 38.432 to 41.568.
D) 39 to 41.

Question

Quizplus · Accepted Answer

To find the 95% confidence interval for the average hourly wage of all information system managers, we will use the formula:

CI = X̄ ± z*(σ/√n)

where X̄ is the sample mean, σ is the population standard deviation, n is the sample size, and z is the z-score corresponding to the desired level of confidence (95% in this case).

Plugging in the given values, we get:

CI = 40 ± 1.96*(8/√100)

CI = 40 ± 1.568

CI = (40 - 1.568, 40 + 1.568)

CI = (38.432, 41.568)

Therefore, the 95% confidence interval for the average hourly wage of all information system managers is (38.432, 41.568). The closest choice to this interval is (C) 38.432 to 41.568.

A Sample of 100 Information Systems Managers Had an Average