1. Confidence Intervals for Proportions

2. The Random Variable –Normal distribution –Mean  = p –Standard Deviation =

3. Confidence Intervals For p (Point Estimate)  z  /2 (Appropriate St’d Deviation) xn Suppose there are x successes in a sample of size n POINT ESTIMATE: APPROPRIATE ST’D DEV.: APPROXIMATE BY: CONFIDENCE INTERVAL:

4. EXAMPLE Taste test between Coke and Pepsi 1000 cola drinkers tested 540 say they prefer Coke Give a 95% confidence interval for the proportion of cola drinkers who favor Coke. Note:

5. Confidence Interval For p – The Proportion That Favor Coke 95% confidence interval:

6. Constructing Confidence Intervals for p Using Excel Suppose cell C5 contains n, cell C7 contains α and cell C9 contains CONFIDENCE INTERVAL: C9 NORMSINV(1-C7/2) SQRT(C9*(1-C9)/C5)

7. 1000 Count the number of alphanumeric observations =COUNTA(A2:A1001) 540 Count the number of “COKE” observations =COUNTIF(A2:A1001, “COKE”).05 α of the (1-α)x100% Confidence Interval.54 x/n =C6/C5 0.50911 =C9-NORMSINV(1-C7/2)*SQRT(C9*(1-C9)/C5) Highlight C11 and press F4 to add $ signs Drag to C12 and change the “-” to a “+” 0.57089

8. Review The point estimate for p is: The confidence interval for p is: Use of Excel (COUNTA, COUNTIF Functions)