STAT 3120 Statistical Methods I Lecture 2 Confidence Intervals

STAT 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?

STAT Confidence Intervals The first category of inference – estimation – is most commonly used to develop Confidence Intervals. A Confidence Interval around a population parameter is developed using: x  z  /2 * (s/SQRT(n)) Where: x = sample mean z  /2 = the appropriate two sided Z-score, based upon desired confidence s = sample standard deviation n = number of elements in sample

STAT Confidence Intervals For example, lets say that we took a poll of 100 KSU students and determined that they spent an average of $225 on books in a semester with a std dev of $50. Report the 95% confidence interval for the expenditure on books for ALL KSU students.

Now, assuming that you need to maintain this MOE, but at a 99% confidence, what is the new sample size? You can do the algebra yourself, or use the following transformation of the formula: n=(z) 2 *δ 2 /E 2 Where: n=sample size z = z-score associated with selected alpha δ = standard deviation (of sample or population) E = Maximum Margin of Error/Width of interval STAT Confidence Intervals

(From Page 201) What if I wanted to be 90% confident? What if I wanted to be 95% confident? What if I wanted to be 99% confident? Typical Z scores used in CI Estimation: 90% confidence = % confidence = % confidence = % confidence = STAT Confidence Intervals

A Confidence Interval around a population proportion is developed using: p  z  /2 * SQRT((pq/n)) Where: p = sample proportion z  /2 = the appropriate two sided Z-score, based upon desired confidence q = 1-p n = number of elements in sample

STAT Confidence Intervals 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.

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

FUN SPSS AND SAS EXERCISES!