STAT 4030 – Programming in R STATISTICS MODULE: Confidence Intervals Jennifer Lewis Priestley, Ph.D. Kennesaw State University 1

STATISTICS MODULE Basic Descriptive Statistics and Confidence Intervals Basic Visualizations Histograms Pie Charts Bar Charts Scatterplots Ttests One Sample Paired Independent Two Sample ANOVA Chi Square and Odds Regression Basics 2 2 2

Sample estimate + conf. level * standard error Statistics Module: Confidence Intervals Any Confidence Interval can be estimated using the following general form: Sample estimate + conf. level * standard error A Confidence Interval around a single population mean is developed using: 𝒙 ±𝒛∗𝒔/ 𝒏 Where: x = sample mean z = the appropriate two sided Z-score, based upon the desired level s = sample standard deviation n = number of elements in sample 3

Statistics Module: Confidence Intervals Typical Z scores used in CI Estimation: 90% confidence = 1.645 95% confidence = 1.96 98% confidence = 2.33 99% confidence = 2.575 4

Statistics Module: Confidence Intervals For example, lets say that we took a poll of 100 college 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 college students. 5

Statistics Module: Confidence Intervals In this example, 𝑥 = 225 z= 1.96 s = 50 n= 100 So, the 95% interval would be: 225 ±1.96∗ 50 100 = 225± 9.8 If the confidence level goes up or down, how does that impact the interval? 6

Statistics Module: Confidence Intervals One general note regarding Confidence Intervals… The results tell us NOTHING about the probability of an individual observation…a 95% interval SHOULD NOT be interpreted as “Joe has a 95% probability of spending between $215.20 and $234.80”. The interval is an estimation of the mean of the population…not of an individual observation. 7