Sample Size Excel Growing Knowing com 2020 1

Sample size �How big should a sample be for a valid study? �Why phone

Formula �Sample size for means: �Sample size for proportion: �Where �n = sample size

Sample Size for Means �Example: what is the sample size required if the standard

Calculating z �Calculate z if confidence level is 96% �Alpha = 1 -. 96

�What is the sample size required if the standard deviation (S. D. ) is

�What sample size is needed for a survey of the time to fly to

Common errors �Most common error is to forget the last step: power of 2.

Sample size for proportion �What should the sample size be if proportion is 59%,

Practise �Go to the website, do Sample Size. Growing. Knowing. com © 2011 10

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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 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. Growing. Knowing. com © 2011 2

Formula �Sample size for means: �Sample size for proportion: �Where �n = sample size �z = normal table �σ = standard deviation �E = allowed error �p = population proportion Growing. Knowing. com © 2011 3

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’ Growing. Knowing. com © 2011 4

�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. 054 �Formula 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. Growing. Knowing. com © 2020 6

�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? �= 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. Growing. Knowing. com © 2020 7

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) Growing. Knowing. com © 2011 8

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 Growing. Knowing. com © 2020 9