Question

An IQ test is designed so that the mean is 100 and the standard deviation is

7

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

99​%

confidence that the sample mean is within

2

IQ points of the true mean. Assume that

σ=7

and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

The required sample size ______ (round up to the nearest integer.

Is this a reasonable sample size for a real world calculation? ______

Answer 1

we have the following values given in the question

Confidence level = 99%

Using z distribution table for 99% confidence level, we get z critical value = 2.576

Margin of error (ME) = 2

We have to find the sample size n for the following data. Formula for the sample size n is given as

Rounding it off to next whole number, we get

sample size n = 82

This is not reasonable sample size for a real world calculation because it is too small as a sample when we compare it with population of normal adults.