Cogito
AP Statistics · Chapter 6 · Lesson 1
Sampling Distributions
How a statistic varies from sample to sample.
12 problems · about 22 minutes · UNC-3.H, UNC-3.I
What this lesson teaches
The student describes the sampling distribution of a statistic and its centre and spread.
- A sampling distribution describes how a statistic varies across samples.
- An unbiased statistic centres on the true parameter.
- The standard error shrinks with the square root of the sample size.
Warm Up
Straightforward practice. Get the method working first.
5 problemsSigma 15, n = 25. What is the standard error of the mean?
Answer 3
Why 3.
What does a sampling distribution describe?
Answer How a statistic varies across all possible samples.
Why The variation of a statistic from sample to sample.
Sigma 30, n = 9. Standard error of the mean?
Answer 10
Why 30 ÷ 3.
Sigma 12, n = 36. Standard error?
Answer 2
Why 12 ÷ 6.
Quadrupling n does what to the standard error? 1 halves it, 2 quarters it.
Answer 1
Why The square root.
Build It Up
The same ideas with more to keep track of.
3 problemsA value describing a population. 1 parameter, 2 statistic.
Answer 1
Why P for population.
Is the sample mean unbiased for the population mean? 1 yes, 0 no.
Answer 1
Why It centres on the truth.
Sigma 50, n = 25. Standard error?
Answer 10
Why 50 ÷ 5.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each description by which distribution it refers to.
Answer A distribution of individuals: The population, One sample of data · A distribution of statistics: The sampling distribution of the mean, All possible sample means for a given n
Why Two of these hold individual measurements.
Sigma 8, n = 64. Standard error?
Answer 1
Why 8 ÷ 8.
The Standard Error: Population standard deviation 20, sample size 100. What is the standard error of the mean?
Answer 2
Why 2.
The Larger Sample: Same population, sample size 400. What is the standard error?
Answer 1
Why 1.