Distinguish between a parameter and a statistic.
Create a sampling distribution using all possible samples from a small population.
Determine if a statistic is an unbiased estimator of a population parameter.
Activity: What was the average for the Chapter 6 Test?
In this Activity, students will be trying to estimate the mean test score for a population using a the mean calculated from a sample. We start with a very simple and unrealistic population of 4 students. We do this to help students build the idea that a sampling distribution contains allof the possible samples from the population (easy to do with such a small population). Tomorrow we will be more realistic and look at the actual population of all AP Stats students.
Where are we headed?
Notice the organization of this Chapter.
Section 7.1 is an introduction to sampling distributions, which includes sampling distributions for proportions and sampling distributions for means. Actually it includes sampling distributions for any statistic.
Section 7.2, we investigate the shape, center, and variability of the sampling distribution of a sample proportion.
Section 7.3, we investigate the shape, center, and variability of the sampling distribution of a sample mean.
The Activity uses a sampling distribution for a sample mean. The Check Your Understanding problem uses a sampling distribution for a sample proportion.
Have I seen this before?
This is not our students first experience with sampling distributions. We have intentionally given them previous experiences in preparation for today’s lesson. In Chapter 4, we took samples of 5 words from from Beyonce’s Crazy in Love in order to estimate the mean word length. We also took samples of Justin Timberlake fans to find the mean enjoyment level. Hopefully you made dotplot posters for these activities and you can refer back to them in this Chapter.
Starting right now, we are going to be crazy about using the correct notation. Notation is wonderful because we can show several ideas at once (is this value from a sample or a population?, is this value a mean or a proportion?).
Population distribution, distribution of a sample, or a sampling distribution?
All three of these distributions can be represented with a dotplot in the Activity. In a population distribution (#1), each dot represents one individual from the population (and we have a dot for every individual). In a distribution of a sample, each dot represents one individual from the population (but we don’t have every individual…only a sample of 2). In a sampling distribution (#4), each dot represents a sample from the population and a mean calculated from that sample.The common error that students make is to use the term “sample distribution” when they mean “sampling distribution”. A sample distribution is the distribution of values for one sample. A sampling distribution represents many, many samples.