pp.157-163 fall 2009

Pp.157-163 fall 2009 - 157 Determining the Sample Size How do we determine how large a sample to take When we are constructing confidence intervals

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Determining the Sample Size How do we determine how large a sample to take? When we are constructing confidence intervals, the sample size, n, can be determined if we specify the confidence level and margin of error (called ‘E’) in our estimate. Margin of Error = E = α/2 ± z n σ The margin of error reflects the precision of the estimate. Obviously, you would like your confidence interval to be as precise (i.e., narrow) as possible. What determines the size of the margin of error? 1. The greater the confidence (the bigger the z- score), the bigger the margin of error 2. The bigger the sample size, n , the smaller the margin of error 3. The bigger the standard deviation, the bigger the margin of error 157 α/2 ± z n Confidence Level Standard Deviation Sample Size
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We can control 1. and 2. We really can not do anything about 3. As it turns out, our strategy will be to determine the sample size, n, that we need for a given level of confidence and a given margin of error (E). The formula for doing this is: ( 29 2 2 / 2 2 z n E α σ = Example : The management for Royale Cinemas would like to determine the mean amount a movie customer spends on refreshments in a single trip to the movies. He would like to estimate µ to within
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This note was uploaded on 06/06/2011 for the course MGSC 291 taught by Professor Rollins during the Fall '09 term at South Carolina.

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Pp.157-163 fall 2009 - 157 Determining the Sample Size How do we determine how large a sample to take When we are constructing confidence intervals

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