Question

True or False: The population of incomes in a particular community is thought to be highly right-skewed with a mean equal to $36,789 and a standard deviation equal to $2,490. Based on this, if a sample of size n = 36 is selected, the highest sample mean that we would expect to see would be approximately $38,034.

Answer 1

Sample mean = = $38,034

= $36,789

=  $2,490

Standard error of sample mean, se = / = 2490 / = 415

z value for sample mean is,

z = ( - ) / se = (38034 - 36789) / 415 = 3

We can have values of z greater than 3 for a highly right-skewed distribution because of long right tail. Thus the statement that the highest sample mean that we would expect to see would be approximately $38,034 is False.