Estimating Population Mean with Known Standard Deviation

Consider an example wherein a truck container is to be redesigned to accommodate longer oakwood logs.

The container is designed based on obsolete measurements, so engineers require a new mean length of the logs.

As getting measurements of all the oakwood trees or logs in the world is impossible, samples can be drawn from the available stock.

This is the sample mean, which is the best point estimate of the population mean when its standard deviation is small.

However, the confidence interval can provide a more reliable estimate of the population mean, which requires calculating the margin of error using the following equation.

If the population and samples both assume the normal distribution, and the sample size is more than 30, a critical value can be obtained using the z distribution.

However, determining the population mean with these assumptions requires prior knowledge of population standard deviation, which is an unrealistic situation.

In the example of oakwood logs, previous forestry studies may provide this standard deviation to calculate the margin of error.