Cogito
AP Statistics · Chapter 4 · Lesson 2
Confidence Intervals for a Mean
Estimating a population mean from a sample.
12 problems · about 22 minutes · UNC-4.R, UNC-4.S
What this lesson teaches
The student constructs and interprets a t-interval for a population mean.
- Use t when the population standard deviation is unknown.
- Degrees of freedom are n − 1 for one sample.
- The interval is the mean plus or minus t times s ÷ √n.
Warm Up
Straightforward practice. Get the method working first.
5 problemss = 15 and n = 25. What is the standard error?
Answer 3
Why 3.
Why use t rather than z for a mean?
Answer The standard deviation is estimated from the sample, which adds uncertainty.
Why The estimated standard deviation.
s = 12, n = 36. Standard error?
Answer 2
Why 12 ÷ 6.
A sample of 40. Degrees of freedom?
Answer 39
Why n − 1.
Mean 50, margin of error 4. Lower end of the interval?
Answer 46
Why 50 − 4.
Build It Up
The same ideas with more to keep track of.
3 problemsAn interval runs from 46 to 54. What is the sample mean?
Answer 50
Why The midpoint.
That interval. What is the margin of error?
Answer 4
Why Half the width.
Which distribution has heavier tails? 1 t, 2 z.
Answer 1
Why The one accounting for an estimated spread.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich interpretation of 95% confidence is correct?
Answer About 95% of intervals built this way capture the true mean.
Why The confidence describes the procedure.
s = 20, n = 100. Standard error?
Answer 2
Why 20 ÷ 10.
The Standard Error: s = 10 and n = 25. What is the standard error?
Answer 2
Why 2.
The Degrees of Freedom: A sample of 25. What are the degrees of freedom?
Answer 24
Why 24.