a. A regional council wants to estimate the mean household water usage over the

Question

a. A regional council wants to estimate the mean household water usage over the past year for the 3,000 households in one of its rural towns. The records are in a bit of a so this mess will involve substantial manual work. They decide to use only a sample of households. In a small pilot study, the mean usage was 164 thousand litres and the standard deviation was 25 thousand litres. How large a sample of households should be taken if we want the margin of error of our estimated mean to be no larger than 2 thousand litres?

Explanation / Answer

Answer to the question)

The Mean (x bar) = 164

Standard deviation (s) = 25

Margin of error (d) = 2

.

Z = 1.96 (standard value for 95% confidence level)

.

The formula of sampel size is :

n = (Z * s / d)^2

n = (1.96 * 25 / 2)^2

n = 600.25

Thus sample size must be 601 units

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