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Confidence Intervals for Proportions

Confidence Intervals for Proportions. The Random Variable. Normal distribution Mean  = p Standard Deviation =. Confidence Intervals For p. (Point Estimate)  z /2 (Appropriate St’d Deviation) Suppose there are x successes in a sample of size n

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Confidence Intervals for Proportions

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

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

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

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