1. Confidence Interval (CI) for the Mean When σ Is Known
MM4D2
Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

2. Definition
A confidence interval is a specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate.
The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter, assuming that a large number of samples are selected and that the estimation process on the same parameter is repeated.

3. Point Estimate
A point estimate is a specific numerical value estimate of a parameter.
The best point estimate of the population mean µ is the sample mean

4. Calculating critical values Z* or Zα/2
Z* or Zα/2 = 1 – { (1- CL decimal form)/2}
Look for the closest number to that value in the body of the z-score table
Then write down the number to the far left and all the way at the top of that value.
Find the critical value of the following:
a) 92% =
b) 94% =
c) 98% =

5. Critical value solution
92% ≈ 1.75
94% ≈ 1.88
98% ≈ 2.33

6. Common critical values Z* or Zα/2

7. Margin of error ME

8. Distribution of

9. Formula for the Confidence Interval of the Mean for a Specific α When σ is Known

10. Example
The following data represent a sample of the assets (in millions of dollars) of 30 credit unions in southwestern Pennsylvania. Find the 90% confidence interval of the mean.

11. Example Solution

12. Solution continues

13. Instructions for finding the mean and standard deviation for a TI-83/84