The Economist Numbers Guide (6th Ed): The Essentials of Business Numeracy (Economist Books) by The Economist

Author:The Economist
Language: eng
Format: mobi, azw3
Publisher: PublicAffairs
Published: 2014-01-27T14:00:00+00:00

Figure 6.1 The mean ±1.96 standard deviation

Confidence

Confidence levels

There is 95% confidence that:

sample mean = population mean ±

[1.96 × (population standard deviation ÷ sample size)]

or, since the same arithmetic works in reverse, there is 95% confidence that:

population mean = sample mean ±

[1.96 × (sample standard deviation ÷ sample size)]

This is exceedingly simple to put into practice. Say you take a random sample of 49 wage rates in a large company, and calculate that the average is $500 with standard deviation of $28. You can say with 95% confidence that the:

population mean wage = sample mean wage ±

[1.96 × (sample standard deviation ÷ sample size)]

= $500 ± [1.96 × ($28 ÷ 49)] = $500 ± $7.84

From this small sample, you are 95% certain that the average wage in the company is between $492 and $508. (See also Sample sums box.)

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