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Cogito

AP Statistics · Chapter 4 · Lesson 2

Practice Worksheet

Confidence Intervals for a Mean

Estimating a population mean from a sample.

12 problems · about 22 minutes · UNC-4.R, UNC-4.S

NameDate

Figure — use these to answer the problems

A sample summarised. The interval is built from its mean and spread, widened by the sample size.
020
  • Minimum8
  • Lower quartile8.50
  • Median10
  • Upper quartile11.50
  • Maximum12
  • Interquartile range3
Value 18
Value 29
Value 310
Value 411
Value 512
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. s = 15 and n = 25. What is the standard error?

    Answer

  2. Why use t rather than z for a mean?

    • The standard deviation is estimated from the sample, which adds uncertainty.
    • Because samples are always small.

  3. s = 12, n = 36. Standard error?

    Answer

  4. A sample of 40. Degrees of freedom?

    Answer

  5. Mean 50, margin of error 4. Lower end of the interval?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. An interval runs from 46 to 54. What is the sample mean?

    Answer

  2. That interval. What is the margin of error?

    Answer

  3. Which distribution has heavier tails? 1 t, 2 z.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Which interpretation of 95% confidence is correct?

    • About 95% of intervals built this way capture the true mean.
    • There is a 95% chance the true mean lies in this interval.

  2. s = 20, n = 100. Standard error?

    Answer

  3. The Standard Error

    s = 10 and n = 25. What is the standard error?

    Answer

  4. The Degrees of Freedom

    A sample of 25. What are the degrees of freedom?

    Answer