1. Confidence Intervals for a Population Mean, Standard Deviation Known

2. Assumptions 1. Sigma, aka population standard deviation is known
2. n > 30 (large sample) or population follows a normal distribution
3. Sample is a simple random sample (equal chance of being selected)

3. Definitions
Point estimate = a single value (or point) used to approximate a population parameter. Note: sample mean is the best point estimate of the population mean
Confidence interval = a range or an interval of values used to estimate the true value of a population parameter

4. Definitions
Margin of error = diff. between observed sample mean and the true value of the population mean “E” aka “maximum error of the estimate”

5. Interpreting a confidence interval
We are 95% confident that the interval from to actually does contain the true value of the population mean.

6. TI-83/84 Instructions TI-83 Finding confidence intervals
1. “Stat” button
2. Choose “Tests” Menu
3. Choose “ZInterval”
4. Highlight “Stats”
5. Enter std dev, mean, n, and C-level
6. “Highlight Calculate” and press “Enter”
Finding Margin of Error : Subtract smallest part of interval from mean.

7. Sample Size to Estimate Population Mean
= critical z score based on desired degree of confidence
E = desired margin of error
= population standard deviation

8. Example 01 Finding critical z score:
Lets find the critical z score for 96% confidence

9. Example 01 Finding critical z score:
Lets find the critical z score for 96% confidence

10. Example 01 Finding critical z score:
We are trying to find the z, so looking at it from left to right, we are interested in 98% or

11. Example 01 Finding critical z score:
So we find it by using:
INVNORM(.98,0,1) =

12. Range Rule of Thumb: If Sigma Isn’t Given
Note: When finding the sample size, always round up if any decimals

13. Confidence Interval (By Hand)