SCENARIO 7-2
The mean selling price of new homes in a small town over a year was $115,000.The population standard deviation was $25,000.A random sample of 100 new home sales from this city was taken.
-Referring to Scenario 7-2,without doing the calculations,state in which of the following ranges the sample mean selling price is most likely to lie?
A)$113,000 -- $115,000
B)$114,000 -- $116,000
C)$115,000 -- $117,000
D)$116,000 -- $118,000

Question

Quizplus · Accepted Answer

Since the sample size is large (n=100), we can use the central limit theorem to assume that the distribution of sample means will be approximately normal. The mean of the sample means will be equal to the population mean ($115,000$) and the standard error of the mean will be equal to the population standard deviation divided by the square root of the sample size ($\frac{\$25,000}{\sqrt{100}}$ or $\$2,500$). This means that 68% of the sample means will fall within one standard error of the mean from the population mean, or between $\$112,500$ and $\$117,500$. Since option B contains this range, it is the most likely range for the sample mean to lie in.

SCENARIO 7-2 The Mean Selling Price of New Homes in a Small