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 7 IQ points of the true mean. Assume that o = 19 and
determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Answer 1

Explanation:

To solve this question, we use this formula:

x± s t_(1−c)/2 / √n = 5

(1 - c)/2 = (1 - 0.95) / 2 = 0.025

Using a 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