Question

"In order to estimate the average electric usage per month, a sample of 33 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 106 kilowatt hours. At 99% confidence, compute the upper bound of the interval estimate for the population mean."

Answer 1

2,157.89 KWH is the upper bound of the interval estimate for the population mean.

Explanation:

We are given the following in the question:

Sample mean,
`\bar{x}` = 2,000 KWH

Sample size, n = 33

Alpha, α = 0.01

Population standard deviation, σ = 106 KWH

99% Confidence interval:

`\mu \pm z_(critical)(\sigma)/(√(n))`

Putting the values, we get,

`z_(critical)\text{ at}~\alpha_(0.01) = 2.58`

`2000 \pm 2.58((106)/(√(3)) )\\\\ = 2000 \pm 157.89 \\\\= (1842.11,2157.89)`

2,157.89 KWH is the upper bound of the interval estimate for the population mean