Statistics / Unit 8: Sampling Distributions and Confidence Intervals
8.1 Sampling Variability
Notes
A parameter describes a population and is fixed. A statistic describes a sample and changes from sample to sample. This natural change is sampling variability.
- The sampling distribution of a statistic is the distribution of its values over all possible samples of the same size from the same population.
- Larger samples give statistics that vary less from sample to sample.
- Random sampling lets us predict how much a statistic will typically vary.
- Example: Two random samples of 100 students from the same school give $52\%$ and $47\%$ who prefer a later start. This difference is expected.
Practice
Two random samples of 100 students from the same school give $52\%$ and $47\%$ who prefer a later start. The best explanation for the difference is:
Different random samples give different statistics even from the same population.
The sampling distribution of a statistic is:
It describes how the statistic varies from sample to sample.
Compared with samples of size 50, samples of size 500 from the same population give statistics that are:
Larger samples reduce sampling variability.
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