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Oksana_A [137]
3 years ago
9

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determi

ned. Assume a population standard deviation of 450 kilowatt-hours. If the sample mean is 1858 kWh, the 95% confidence interval estimate of the population mean is
Mathematics
1 answer:
lana [24]3 years ago
6 0

Answer:

Confidence interval:  (1760,1956)

Step-by-step explanation:

We are given the following information in the question:

Sample size, n = 81

Sample mean =

\bar{x} = 1858 \text{ kWh}

Population standard deviation =

\sigma = 450 \text{ kilowatt-hours}

Confidence Level = 95%

Significance level = 5% = 0.05

Confidence interval:

\bar{x} \pm z_{critical}\displaystyle\frac{\sigma}{\sqrt{n}}

Putting the values, we get,

z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96

1858 \pm 1.96(\displaystyle\frac{450}{\sqrt{81}} ) = 1858 \pm 98 = (1760,1956)

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