The population of incomes in a community college in Iowa is thought to be highly skewed to the right with a mean equal to $38,765 and a standard deviation equal to $2,640. Based on this information, if a sample of size 36 is selected at random, then the highest sample mean that we would expect to see would be approximately $40,085.

Question

Quizplus · Accepted Answer

This statement is true based on the central limit theorem, which states that as sample size increases, the distribution of sample means will approach a normal distribution regardless of the underlying population's distribution. Therefore, the highest sample mean that we would expect to see can be calculated using the formula:

highest sample mean = population mean + (z-score x standard error)

Assuming a significance level of 0.05 (corresponding to a z-score of 1.645), the standard error would be:

standard error = standard deviation / square root of sample size
standard error = 2640 / sqrt(36)
standard error = 440

Substituting these values into the formula, we get:

highest sample mean = 38765 + (1.645 x 440)
highest sample mean = 40085

Therefore, the statement is true.

The Population of Incomes in a Community College in Iowa