Question

A study has indicated that the sample size necessary to estimate the average electricity use by residential customers of a large western utility company is 900 customers. Assuming that the margin of error associated with the estimate will be ±30 watts and the confidence level is stated to be 90 percent, what was the value for the population standard deviation?

Answer 1

`\sigma=547.1125`

Explanation:

-The margin of error is calculated using the formula:

`ME=z_(\alpha/2)* (\sigma)/(√(n))\\\\`

-We substitute the values, n=900 and ME=30 in the formula to solve for standard deviation:

`ME=z_(\alpha/2)* (\sigma)/(√(n))\\\\\\30=1.645*(\sigma)/(√(900))\\\\\sigma=(30^2)/(1.645)\\\\=547.1125`

Hence, the population standard deviation is 547.1125