What is a Sampling Distribution? Day 2
Day 66 - Lesson 7.1
Use the sampling distribution of a statistic to evaluate a claim about a parameter.
Determine if a statistic is an unbiased estimator of a population parameter.
Describe the relationship between sample size and the variability of a statistic.
Activity: What was the average for the Chapter 6 test?
Just like the lesson from yesterday, students will be trying to estimate the mean Chapter 6 test score using a sample mean (statistic). Today we are looking at the much more realistic population of all AP Stats students (85 this year at East Kentwood High School!) You will need to have your Chapter 6 Test scores (no names!) available to give to students for this Activity.
"What does this dot represent?"
In the Activity, students create a dotplot on a posterboard at the front of the room. Once completed, point at one of the dots and ask students “What does this dot represent?”. The ideal response is “a sample of 5 test scores and an average calculated from that sample”. Then point to another dot and ask again “What does this dot represent?”. Students should respond with “A different sample of 5 test scores and an average calculated from that sample”. In the end, they recognize that a sampling distribution represents many, many samples of 5 test scores and an average calculated for each.
Bring it back to Beyonce
Remind students on this Activity from Chapter 4. We were trying to estimate the average word length from Crazy in Love by Beyonce, so that we could evaluate the claim that she did not write the lyrics. The first sampling method had students quickly circle five words and find the mean. It is likely that most of your students overestimated the true mean word length. Put another way, the mean of the sampling distribution was much greater than the true mean of the population. This is exactly the definition of a biased statistic.
We then tried a second approach (using an SRS) which did produce an unbiased statistic (hopefully just like your students estimates of the Chapter 6 test average from the activity today).