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5.3 Determining Sample Size to Estimate p

5.3 Determining Sample Size to Estimate p. 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?

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5.3 Determining Sample Size to Estimate p

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  1. 5.3 Determining Sample Size to Estimate p

  2. 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 ofError.

  3. Required Sample Size n to Estimate a Population Proportion p

  4. Confidence level Sampling distribution of .95

  5. What About p and q=1-p?

  6. 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

  7. Example: Sample Size to Estimate a Population Proportion p (cont.)

  8. 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?

  9. 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:

  10. 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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