Question

Question Help An IQ test is designed so that the mean is 100 and the standard deviation is 18 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 8 IQ points of the true mean. Assume that a = 18 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 is (Round up to the nearest integer.) Would it be reasonable to sample this number of students? No. This number of IQ test scores is a fairly small number No. This number of IQ test scores is a fairly large number. Yes. This number of IQ test scores is a fairly large number Yes. This number of IQ test scores is a fairly small number OOOO Click to select your answer(s).

Answer 1

Solution:

Given ,

$\sigma$ = 18 ..Population SD

E = 8 Margin of error

c = 99% = 0.99 ...confidence level

$\therefore$$\alpha$ = 1- c = 1- 0.99 = 0.01

$\therefore$  $\alpha$/2 = 0.005

Using Z table ,

$\therefore$ = 2.576   

2012

Now, sample size (n) is given by,

"a/2 * o n n = E

=  {(2.576* 18 )/ 8 }²

= 33.59

= 34 ..(round to the next whole number)

The required sample size is 34

Yes , This number of IQ test scores is a fairly small number.