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Published byNeal Cunningham Modified over 9 years ago
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5.3 Determining Sample Size to Estimate p
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To Estimate a Population Proportion p If you desire a C% confidence interval for a population proportion p with an accuracy specified by you, how large does the sample size need to be? We will denote the accuracy by ME, which stands for Margin of Error.
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Required Sample Size n to Estimate a Population Proportion p
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.95 Confidence level Sampling distribution of
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What About p and q=1-p?
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Example: Sample Size to Estimate a Population Proportion p The U. S. Crime Commission wants to estimate p = the proportion of crimes in which firearms are used to within.02 with 90% confidence. Data from previous years shows that p is about.6
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Example: Sample Size to Estimate a Population Proportion p (cont.)
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Example: Sample Size to Estimate a Population Proportion p The Curdle Dairy Co. wants to estimate the proportion p of customers that will purchase its new broccoli-flavored ice cream. Curdle wants to be 90% confident that they have estimated p to within.03. How many customers should they sample?
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Example: Sample Size to Estimate a Population Proportion p (cont.) The desired Margin of Error is ME =.03 Curdle wants to be 90% confident, so z*=1.645; the required sample size is Since the sample has not yet been taken, the sample proportion p is still unknown. We proceed using either one of the following two methods:
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Example: Sample Size to Estimate a Population Proportion p (cont.) Method 1: – –There is no knowledge about the value of p – –Let p =.5. This results in the largest possible n needed for a 90% confidence interval of the form – –If the proportion does not equal.5, the actual ME will be narrower than.03 with the n obtained by the formula below. Method 2: –There is some idea about the value of p (say p ~.2) –Use the value of p to calculate the sample size
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