Determining the Sample Size for Estimating p. The Confidence Interval (Point Estimate)  z  /2 (Appropriate St’d Deviation) The confidence interval is:

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Presentation transcript:

Determining the Sample Size for Estimating p

The Confidence Interval (Point Estimate)  z  /2 (Appropriate St’d Deviation) The confidence interval is:

What Should Be Used For p? If there is some idea -- use this value If there is no idea -- take “worst case” scenario –Worst case is where the standard deviation is as large as it can get –This happens when p =.5

Example How large a sample must be drawn to estimate the true percentage of Coke drinkers to within .04 (with 95% confidence) if: –(1) Last week a similar survey found that 60% favored Coke –(2) There is no estimate for the percentage of Coke drinkers The 95% confidence interval is

Case 1 A Recent Estimate For p Was p =.6 Use p =.6 in the 95% confidence interval. The “  ” part must =.04. Thus,

Case 2 There Is No Estimate For p Use p =.5 in the 95% confidence interval The “  ” part must =.04. Thus,

Review To determine a value for n so that p is estimated to within ±E with confidence 1-α, solve for n in the formula: If there is an estimate for p, use it. If there are no estimates for use p =.5.