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Sample sizeHow big should a sample be for a valid study?Why phone 10,000 students if phoning 50 is

enough?Large samples take longer and cost more

What if a sample of 50 is not enough, you need 51 for a valid study?

We will learn how to calculate the needed sample size.

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FormulaSample size for means:

Sample size for proportion:

Wheren = sample sizez = normal table σ = standard deviationE = allowed errorp = population proportion

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Sample Size for MeansExample: what is the sample size required

if the standard deviation (S.D.) is 11.55, error is within 3.01, and confidence level is 96%?

Notice error (E) is 3.01Some students have trouble detecting E.Look for words like ‘within’ if it does not say

‘error’Always use z, never use t in sample size

calculations

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Calculating z

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What is the sample size required if the standard deviation (S.D.) is 11.55, error is within 3.01, and confidence level is 96%?

Formula

n = (2.055 x 11.55 / 3.01)2 = 7.885452 = 62.1 Round up to 63

Why round to 63 from 62.1? Not what we were taught rounding in arithmetic!

You cannot talk to .1 of a person, so to have a valid study with 62.1 or more in your sample, you are forced to round up.

Rule: Always round up in Sample Size.

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What sample size is needed for a survey of the time to fly to Basra, Iraq from New York. You want the time to be within 15.73 minutes with 94% confidence. Standard deviation is 43.7 minutes.

What is the error?E = 15.73

What is z?z = (confidence /2 ) = .94 /2 = .4700Lookup z in table = 1.88

n = (1.88 x 43.7 / 15.73)2 = 27.3Sample size, always round up. Answer n = 28.

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Common errorsMost common error is to forget the last step: power

of 2. If the number looks small, double check power of 2.

You don’t see the error value.Look for ‘within’

In a test, after doing many probability questions, you may be looking for a probability question when you are being asked for a Sample Size calculation!

Last common error, you don’t understand there are 2 formulas for sample size (1st is Means, 2nd is proportion)

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Sample size for proportionWhat should the sample size be if proportion is

59%, error is 0.17, and confidence level is 0.92?

Formula =

n = .59(1 - .59)(z / .17)2 z = (confidence /2 ) = (.92 /2 ) = .4600Lookup .4600, z = 1.75

n = .59(1 - .59)(1.75 / .17)2 = .59 x .41 x 105.9688581 = 25.63

Answer = 26

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PractiseGo to the website, do Sample Size.

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