107 5 20 58 2 2 \u00b9 n Sample Size Determination for a Variable Another Example

# 107 5 20 58 2 2 ¹ n sample size determination for a

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107 5 ) 20 )( 58 . 2 ( 2 ! ¸ ¹ · ¨ © § ! n Sample Size Determination for a Variable- Another Example
Sample Size for Estimating a Population Proportion n p p z E ) 1 ( 0 ! where: n is the size of the sample z is the standard normal value corresponding to the desired level of confidence E is the maximum allowable error 313 2 ) 1 ( ¸ ¹ · ¨ © § 0 ! E z p p n Selecting an Appropriate Sample Size -- Estimating the Proportion There are a few options to estimate the proportion (when it is unknown prior to the sample). z Use a Comparable Study. z Conduct a Pilot Study. z Use the DEFAULT value of 0.50 . (0.50) * (0.50) = 0.25 (0.40) * (0.60) = 0.24 (0.30) * (0.70) = 0.21 ... (0.01) * (0.99) = 0.0099 313
Example for Sample Size with Proportions The American Kennel Club wanted to estimate the proportion of children that have a dog as a pet. If the club wanted the estimate to be within 3% of the population proportion, how many children would they need to contact? Assume a 95% level of confidence and that the club estimated that 30% of the children have a dog as a pet. 897 03 . 96 . 1 ) 70 )(. 30 (. 2 ! ¸ ¹ · ¨ © § ! n Another Example A study needs to estimate the proportion of cities that have private refuse collectors. The investigator wants the margin of error to be within .10 of the population proportion, the desired level of confidence is 90 percent, and no estimate is available for the population proportion. What is the required sample size? cities 69 0625 . 68 10 . 65 . 1 ) 5 . 1 )( 5 (. 2 ! ! ¸ ¹ · ¨ © § 0 ! n n
GOALS 1.Define a Point Estimate. 2.DefineLevel of Confidence. 3. Construct a confidence interval for the population mean when the population standard deviation is known. 4. Construct a confidence interval for a population mean when the population standard deviation is unknown. 5. Construct a confidence interval for a population proportion. 6.Determine the sample size for attribute and variable sampling.

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