Question

An IQ test is designed so that the mean is 100 and the standard deviation is 22 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 4 IQ points of the true mean. Assume that sigmaequals22 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real-world calculation.

1. The required sample size is?

2. Would it be reasonable to sample this number of students?

a. Yes. This number of IQ test scores is a fairly small number.
b. No. This number of IQ test scores is a fairly large number.
c. No. This number of IQ test scores is a fairly small number.
d. Yes. This number of IQ test scores is a fairly large number.

Answer 1

Solution :

Given that,

Population standard deviation = = 22

Margin of error = E = 4

1)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

sample size = n = (Z_/2* / E) ²

n = (1.96 * 22/ 4)²

n = 116.21

n = 117

Sample size = 117

2)

Option a is correct.