An lQ test is designed so that the mean is 100 and the standard deviation is 14

Question

An lQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean 10 score of statistics students such that it can be said with 99% confidence that the sample mean is within 3 10 points of the true mean. Assume that sigma = 14 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? Yes. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly small number. No. This number of lQ test scores is a fairly large number, Yes. This number of lQ test scores is a fairly small number.

Explanation / Answer

Margin of Error (half of confidence interval) = 3
The margin of error is defined as the "radius" (or half the width) of a confidence interval for a particular statistic.
Level of Confidence = 99
: population standard deviation = 14
('z critical value') from Look-up Table for 90% = 2.57
The Look-up in the Table for the Standard Normal Distribution utilizes the Table's cummulative 'area' feature. The Table shows positve and negative values of ('z critical') but since the Standard Normal Distribution is symmetric, only the magnitude of ('z critical') is important.




For a Level of Confidence = 90% the corresponding LEFT 'area' = 0.45. And due to Table's symmetric nature, the corresponding RIGHT 'area' = 0.45 The ('z critical') value Look-up is 1.64


Margin of Error = ('z critical value') * /SQRT(n)
n = Sample Size

Algebraic solution for n:
n = [('z critical value') * /Margin of Error]²
= [ (2.57 * 14)/3 ]²

Sample Size = 144 for 99% level of confidence

YES THIS NUMBER OF IQ TEST SCORES IS FAIRLY SMALL NUMBER

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