Question

Electricity usage in households is known to be normally distributed with a standard deviation of 73...

Electricity usage in households is known to be normally distributed with a standard deviation of 73 kWh (kilowatt - hours). A random sample of 15 households study on electricity usage, and the number of kWh was recorded for each household in the sample for the first quarter of 2018. The average usage was found to be 275 kWh.

a) Find a 95% confidence interval on the mean.

b) Suppose that we wanted the error in estimating the mean electricity usage from the 95% confidence interval to be 20 kWh. What sample size should be used?

Homework Answers

Answer #1

a)

95% confidence interval for mean is

- z * / sqrt(n) < < + z * / sqrt(n)

275 - 1.96 * 73 / sqrt(15) < mu < 275 + 1.96 * 73 / sqrt(15)

238.057 < < 311.943

95% CI is (238.05 , 311.943)

b)

Sample size = ( Z/2 * / E)2

= ( 1.96 * 73 / 20)2

= 51.18

Sample size = 52 ( rounded up to nearest integer)

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