Question

Use the given information to construct a 99% confidence interval estimate of the mean of the population. n = 39, σ = 3.86, Xbar = 41.7

40.1 < μ < 43.3



40.5 < μ < 42.9



–9.4 < μ < 92.8



41.4 < μ < 42.0

Answer 1

40.1 < μ < 43.3

Explanation:

Margin of error = critical value × standard error

ME = CV × SE

At 99% confidence and 38 degrees of freedom, CV = 2.712.

SE = s / √n

SE = 3.86 / √39

SE = 0.618

So the margin of error is:

ME = 2.712 × 0.618

ME = 1.7

So the 99% confidence interval of the population mean is:

μ = 41.7 ± 1.7

40.0 < μ < 43.4

Closest answer is the first one.