Question

An IQ test is designed so that the mean is 100 and the standard deviation is 19 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 2 IQ points of the true mean. Assume that Ơ = 19 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

(a)The required sample size is ____. (Round up to one integer as needed)
(b)Is this sample size reasonable?

Answer 1

Hello there.
An IQ test is designed so that the mean is 100 and the standard deviation is 19 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 2 IQ points of the true mean. Assume that Ơ = 19 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
(a)The required sample size is ____. (Round up to one integer as needed)
(b)Is this sample size reasonable?

A) 97
B) True/Yes

Answer 2

We use the formula:
x± s t_(1−c)/2 / √n = 5

(1 - c)/2 = (1 - 0.95) / 2 = 0.025
Using the t score calculator at this value, at the 95% confidence internval,
t = 0.5080, So
100 - 19(0.5080) / √n = 5
Solving for n
n = 97

a) 97
b) yes