Question

In a preliminary study of 45 customers, we ask how much they would pay for an upgrade to their water filtration system; for this sample, the average price is 35 with a variance of 400. How many customers would we need to contact in order to be 80% confident that the estimated price will be within 2 euro of the true price?

Answer 1

Solution :

The sample size needed to estimate the population mean within E of the true mean with 80% confidence level is given as follows :

Where, is population standard deviation, E is margin of error and Z(0.20/2) is critical z-value to construct 80% confidence interval.

Since, we want to estimate the price such that it is within 2 euro ef the true mean price, therefore E = 2.

Since, is not known so we shall use it's estimate. In the previous study we have sample variance is 400.

Using Z-table we get, Z(0.20/2) = 1.282

Hence, required sample size is,

On rounding to nearest integer we get,

n = 164

Hence, we need to contact to contact 164 customers in order to be 80% confident that the estimated price will be within 2 euro of the true price.