The population of incomes in a community college in Ontario 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

Since the population is highly skewed to the right, we can expect that samples will also be skewed to the right. Additionally, as the sample size increases, the sample mean becomes more and more representative of the population mean. Therefore, if we take a sample of size 36, the highest sample mean that we would expect to see would be slightly above the population mean, but not substantially higher. Using the formula for the standard error of the mean, we can calculate that the standard error of the mean for a sample of size 36 is approximately $440. This means that we would expect approximately 95% of sample means to fall within two standard errors of the population mean, or between approximately $35,685 and $41,845. Therefore, it is plausible that the highest sample mean we would expect to see is approximately $40,085, and the statement is true.

The Population of Incomes in a Community College in Ontario