1. INCM 9201 Quantitative Methods Confidence Intervals - Proportion

2. Confidence Intervals As you learned previously, Inferential Statistics relies on the Central Limit Theorem. Methods for making inferences are based on sound sampling methodology and fall into two categories: 1. Estimation – Information from the sample can be used to estimate or predict the unknown mean of a population. Example: What is the mean decrease in Cholesterol due to taking Drug A? 2. Hypothesis Testing – Information from the sample can be used to determine if a population mean is greater than or equal to another population or a specified number. Example: Is the mean cholesterol reading for patients taking Drug A lower than the cholesterol reading for a control group?

3. These notes will guide you through estimating proportion confidence intervals. Including: CIs for one population proportions CIs for the difference between two population proportions. In each case: 1.The formula will be presented; 2.The formula will be applied (manually); 3.The formula will be applied via Excel. Confidence Intervals

4. Confidence Intervals - Formula The interval for any CI estimate can be expressed as: Sample estimate + conf. level * standard error In the case of a single population proportion, the expression is: p + Z * SQRT((p(1-p))/n) Where, “p” is the proportion of units in a sample; Z is the associated # of Std deviations associated with the required confidence level; n is the number of obs in the sample.

5. Typical Z scores used in CI Estimation: 90% confidence = 1.645 95% confidence = 1.96 98% confidence = 2.33 99% confidence = 2.575 Can you explain where these numbers come from? Confidence Intervals

6. Confidence Intervals - Application For example, lets say that we took a poll of 100 KSU students and determined that 26% voted Libertarian. Report the 95% confidence interval for the proportion of KSU students expected to vote Libertarian.

7. Now, assuming that you need to maintain this MOE, but at a 99% confidence, what is the new sample size? Confidence Intervals - Application

8. Confidence Intervals - Formula As we saw previously, the interval for any CI estimate can be expressed as: Sample estimate + conf. level * standard error In the case of a CI for the difference between two proportions, the expression is: p 1 –p 2 + Z * SQRT(((p 1 (1-p 1 ))/n 1 )+((p 2 (1-p 2 )/n 2 ))) Where, “p” is the proportion of units in a sample (1 or 2); Z is the associated # of Std deviations associated with the required confidence level; n is the number of obs in the sample (1 or 2).

9. Confidence Intervals - Application For example, lets say that we took a poll of students and asked “would you date someone with a great personality who you were not attracted to?” By gender, the results were 61.1% of 131 women said “yes” while 42.6% of 61 men said “yes”. What is the 95% Confidence Interval? Would you expect the 90% Interval to be larger or smaller? Why?