Question

n order to estimate the average electric usage per month, a sample of 44 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 133 kilowatt hours. At 99% confidence, compute the upper bound of the interval estimate for the population mean.

Answer 1

Answer: 2051.64 kilowatt hours.

Explanation:

Given : Sample size : 44

The sample mean :
`\overline{x}=2,000\text{ KWH. }`

Population standard deviation:
`s\igma= 133\text{ KWH. }`

z-value for 99% confidence interval :
`z_c=2.576`

The upper bound of the 99% confidence interval estimate for the population mean :-

`\overline{x}+z_c(\sigma)/(√(n))`

`2000+(2.576)(133)/(√(44))\\\\=2000+(2.576)(20.05)\\\\=2000+51.6488=2051.6488\approx2051.64`

Hence, the upper bound of the 99% confidence interval estimate for the population mean = 2051.64 kilowatt hours.