Question

Recall the chapter example which described the fact that the mean IQ in large, diverse populations is 100 and the standard deviation is 15. Your sample of 300 members of your community gave you a mean IQ score of 108. Calculate the margin of error for the 99% confidence level for this sample. Which of the following figures comes closest to your answer?

A. 10.95.
B. ±1.96.
C. 12.23.
D. 11.16.
E. None of the above

Answer 1

The margin of error for the 99% confidence level for this sample is ±2.23.

None of the given figures is close to the answer:

E. None of the above

Explanation:

margin of error (ME) around the mean can be calculated using the formula

ME=
`(z*s)/(√(N) )` where

• z is the corresponding statistic of the 99% confidence level (2.576)

• s is the population IQ standard deviation (15)

• N is the sample size (300)

Using these numbers we get:

ME=
`(2.576*15)/(√(300) )` ≈ 2.23