Excel GrowingKnowingcom 2011 1 GrowingKnowingcom 2011 Sample size How big should a sample be for a valid study Why phone 10000 students if phoning 50 is enough Large samples take longer and cost more ID: 553593
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Sample SizeExcel
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Sample size
How 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 moreWhat 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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Formula
Sample size for means:Sample size for proportion:
Wheren = sample sizez = normal table σ = standard deviation
E = allowed error
p = population proportion
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Sample Size for Means
Example: 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 3.01
Some students have trouble detecting E.Look for words like ‘within’ if it does not say ‘error’
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Calculating z
Calculate z if confidence level is 96%Alpha = 1 - .96 = .04z =norm.s.inv(confidence level + (alpha/2))
= norm.s.inv(.96 + .04/2 ) = 2.054
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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
z = norm.s.inv(confidence level + (alpha/2))
=
norm.s.inv
(.96 + .04/2 ) = 2.054Formula for n = (2.054 x 11.55 / 3.01)2
Excel: =(2.054*11.55/3.01)^2 = 7.88545^2
= 62.1
Brackets are important
or you get the wrong answer. Why?We round to 63 from 62.1, but why?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 and Percentile. GrowingKnowing.com © 20206Slide7
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 = 15.73What is z?
= norm.s.inv(confidence level + (alpha/2))= norm.s.inv
(.94 + .06/2 ) = 1.88
Excel n: = (1.88*43.7/15.73)^2 = 27.3
Sample size, always round up. Answer n = 28.
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Common errors
Most 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 (1
st
is Means, 2
nd
is proportion)
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Sample size for proportion
What should the sample size be if proportion is 59%, error is 0.17, and confidence level is 0.92?Formula =
z = norm.s.inv(confidence level + (alpha/2)) = norm.s.inv
(.92 + .08/2 ) = 1.75
Excel n = .59*(1 - .59)*(1.75/.17)^2
= .59 x .41 x 105.9688581 = 25.63
Answer = 26
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Practise
Go to the website, do Sample Size.GrowingKnowing.com © 2011
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