Week 6: Estimating from a sample#
STATS 60 Spring 2025
10 bonus points for attendance
10 bonus points for completing assignment
Discussion assignment (extra credit, bonus points: 10 + up to 5 additional points):#
Look for a recent example of an article or other media piece which makes conclusions based on a poll or other sample estimate where the sample size \(n\) was too small. As usual, the more reputable the source, the better.
In the Google Poll by 07:00 AM on Thursday, May 8:
Upload a screenshot and description of the example.
Explain why you think \(n\) was too small, using the following quantitative criteria:
a. How large is the standard deviation (using an appropriate upper bound on the sample standard deviation, e.g. 1 if the study is a poll)?
b. Do you expect that the Normal approximation applies? If so, what is your confidence that the estimate is within \(\epsilon\) of the mean, for \(\epsilon\) a number of the relevant resolution?
If your example is chosen for presentation in discussion, you get 5 additional bonus points.
Discussion Agenda#
Show and tell (5 minutes)#
The discussion instructor selects the top example of an estimate from a too-small sample size from their section.
The student curator explains their example, and how they determined that \(n\) is too small.
Overview of concepts from the week (10 minutes)#
Discussion instructor reviews key concepts from the week.
Activity: estimating a population mean via the sample mean (25 minutes)#
Students will use samples to estimate a population mean, experiencing how the following factors affect the distribution of the sample mean:
Sample size
Biased samples
Activity:
Each student will be given a 6-sided dice.
For each \(n\) in \(\{10, 20, 30\}\):
Student rolls the dice \(n\) times, then computes the sample mean \(\hat\mu_n\) of dice outcomes.
Student enters values into the poll.
Note: you can just record the outcome of 30 rolls, and then take the mean of the first \(n\) for your \(n\)th sample. That will save you some rolls.
Discussion instructor displays the histogram of sample means for each \(n\).
Biased sample: Repeat steps 1-3 for \(n=20\), but this time, roll two dice for each roll and take the sample to be the value of the smaller of the two numbers.
This biases the outcome against large numbers.
What is the probability that you record a \(6\) for one of your samples?
Recap (10 minutes)#
Students participate in TA led discussion about the activity:
Did variability of the sample mean decrease as expected with \(n\)?
How did the biased sampling affect the estimates?