How large of a sample is required to estimate the mean usage of electricity?

Question

The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.15 kWh. A previous study found that for an average family the standard deviation is 2.5 kWh and the mean is 15.9 kWh per day. If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of electricity?

 

Answer 1

We start with a z-score z^* such that P(|z|< z^*) = 0.85

 

So P(z < -z^*) = (1 - 0.85)/2 = 0.075, which happens at z^* = 1.43953...

 

Thus we want the standard error to be (0.15/1.43953...) = 0.1042... kWh

 

σ/√n = SE ⇒ n = (σ/SE)² = (2.5/0.1042...)² = (23.992...)² = 575.6...

 

We must round up. So we need a sample size of at least 576.