Skip to lesson

Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

AP Statistics · Chapter 6 · Lesson 1

Practice Worksheet

Sampling Distributions

How a statistic varies from sample to sample.

12 problems · about 22 minutes · UNC-3.H, UNC-3.I

NameDate

Figure — use these to answer the problems

Bunch the values and the box narrows. A larger sample narrows a sampling distribution the same way.
020
  • Minimum9
  • Lower quartile9.50
  • Median10
  • Upper quartile11.50
  • Maximum12
  • Interquartile range2
Sample 19
Sample 210
Sample 310
Sample 411
Sample 512
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Sigma 15, n = 25. What is the standard error of the mean?

    Answer

  2. What does a sampling distribution describe?

    • How a statistic varies across all possible samples.
    • How the data varies within one sample.

  3. Sigma 30, n = 9. Standard error of the mean?

    Answer

  4. Sigma 12, n = 36. Standard error?

    Answer

  5. Quadrupling n does what to the standard error? 1 halves it, 2 quarters it.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A value describing a population. 1 parameter, 2 statistic.

    Answer

  2. Is the sample mean unbiased for the population mean? 1 yes, 0 no.

    Answer

  3. Sigma 50, n = 25. Standard error?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each description by which distribution it refers to.

    Write each item under the heading it belongs to: The population · One sample of data · The sampling distribution of the mean · All possible sample means for a given n

    A distribution of individuals

    A distribution of statistics

  2. Sigma 8, n = 64. Standard error?

    Answer

  3. The Standard Error

    Population standard deviation 20, sample size 100. What is the standard error of the mean?

    Answer

  4. The Larger Sample

    Same population, sample size 400. What is the standard error?

    Answer