Auniversity surveyed recent graduates of the english department for their starting salaries. four hundred graduates returned the survey. the average salary was $25,000, with a standard deviation of $2,500. what is the best point estimate of the population mean?

Step-by-step explanation:

Data given

represent the sample mean obtained

represent the sample deviation obtained

represent the true mean (variable of interest)

n=400 represent the sample size selected

Solution to the problem

The best estimator for the true mean is given by the sample mean , and the reason is: If we assume that in tha random sample each observation follows a normal distribution like this:

Then when we find the expected value for the sample mean we have this:

If we use the properties of the expected value we have:

And since the expected value of each observation is the same we have:

So then we have that the best estimator for the population mean is given by:

step-by-step explanation: step 3 should really go to step seven, but anyway never mind.

1 ∠oln ≅ ∠lno