Answer:
(15.9,16.1) is the required 98% confidence interval for mean usage of electricity.
Step-by-step explanation:
We are given the following in the question:
Sample mean, [tex]\bar{x}[/tex] = 16 kWh
Sample size, n = 3394
Alpha, α = 0.02
Population standard deviation, σ = 2.5 kWh
98% Confidence interval:
[tex]\bar{x} \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.02} = 2.33[/tex]
[tex]16 \pm 2.33(\dfrac{2.5}{\sqrt{3394}} )\\\\ = 16 \pm 0.0999 = \\\\(15.9001,16.0999)\approx (15.9,16.1)[/tex]
(15.9,16.1) is the required 98% confidence interval for mean usage of electricity.
