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? We will denote the accuracy by ME, which stands for Margin of Error.

Required Sample Size n to Estimate a Population Proportion p

Sampling distribution of Confidence level .95

What About p and q=1-p?

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

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

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?

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:

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 E 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