Question

A university claims its recent graduates earn an average annual salary of $50,000. You draw a random sample of 30 recent graduates and find that their average salary is $47,000, with a standard deviation of $5,000. What is the estimate of the standard error of the mean for this data?

Answer 1

Answer: $645.50

Explanation:

The standard error of of the mean is given by :-

`SE_x=(s)/(√(n))` ,

where n= sample size .

s= sample standard deviation.

Given : You draw a random sample of 30 recent graduates and find that their average salary is $47,000, with a standard deviation of $5,000.

i.e. n= 60

Samples standard deviation : s= $5,000

Then, the standard error of the mean for this data will be :-

`SE_x=(5000)/(√(60))\\\\=(5000)/(7.74596669)\\\\=645.49722436\approx645.50` [To the nearest cent]

Hence, the estimate of the standard error of the mean for this data = $645.50