1. Chapter 14 - Confidence Intervals: The Basics
Confidence Interval = estimate + margin of error
Purpose is to estimate an unknown population parameter and give some indication of how accurate the estimate is.
ex: Test Scores: (0-500), n=840 people
What is the mean for this test in the population?
According to the Rule, 95% of all samples should have a mean that falls within 2 std. devs. (s) of the population mean
272 is our estimate of the population mean…

2. 2s = 2(2.1) = 4.2
So 95% of all samples should have a mean somewhere between
We call this a “95% Confidence Interval”
margin of error
estimate

3. “Level C” Confidence Interval
C = decimal form of confidence percentage
ex: 95% conf. int. --> C = .95
Definition: An interval computed from sample data by a method that has probability “C” of producing an interval containing the true value of the parameter.”
z* = unknown number of standard deviations to produce a given confidence interval.
ex: Find z* for an 80% confidence interval.

4. Need a z-value with .9 to its left…
80%
90%
Need a z-value with .9 to its left…
10%

5. Calculator Steps
Select STAT--TESTS--#7
Set to the following values:

6. Interval Formula
ex: Blood sample drug concentration
Find a 99% confidence interval…
Z* = 2.576

7. Interval =

8. Confidence Interval Behavior
Margin of Error (m) =
Changing any of the values in the equation will change the margin of error…
The margin of error will decrease when:
z* gets smaller
 gets smaller
n gets larger (4n to reduce m by half…)
ex 14.4, pg 361

9. = 7.1 Choosing the sample size
The confidence interval for a population mean will have a specified margin of error (m) when the sample size is:
ex: Blood sample drug concentration
Produce results accurate to within with 95% confidence… how many measurements will we need to average?
m = .005
z* = 1.96 for C=.95
=.0068
= 7.1
** n generally will need to be whole numbers - so we must take 8 measurements…