1. HMI 7530– Programming in R STATISTICS MODULE: Confidence Intervals
Jennifer Lewis Priestley, Ph.D.
Kennesaw State University 1

2. 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

3. 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

4. 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

5. 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

6. 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∗
= 225± 9.8
If the confidence level goes up or down, how does that impact the interval? 6

7. 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 $ and $234.80”.
The interval is an estimation of the mean of the population…not of an individual observation. 7