Answer:
90% confidence interval: (22.35,23.45)
Step-by-step explanation:
We are given the following in the question:
Sample mean, [tex]\bar{x}[/tex] = 22.9 years
Sample size, n = 20
Alpha, α = 0.10
Population standard deviation, σ = 1.5 years
90% Confidence interval:
[tex]\bar{x} \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.64[/tex]
[tex]22.9 \pm 1.64(\dfrac{1.5}{\sqrt{20}} )\\\\ = 22.9 \pm 0.55 \\\\= (22.35,23.45)[/tex]
(22.35,23.45) is the required 90% confidence interval for population mean age.
