Probability and Statistical Inference

1. Describe the potential bias of one sample and mitigate bias by using multiple random samples. 
2. Distinguish between a population characteristic and a sample statistic, defining the characteristic as what is true about a population and a sample statistic as an estimate of that characteristic based on a smaller, representative group. 
3. Calculate sample statistics such as the sample mean and sample variability between random samples. 
4. Describe the variability of multiple samples and use this information to assess the accuracy in the samples to predict a population characteristic.

• For Anchor Problem #1, the discussion and synthesis will have to be fairly teacher directed. The idea that you could take multiple random samples and compare the means will a big step for many students. Projecting the applet and completing the suggestions that students have for how the sampling size and number of samples drawn in real time in front of the class will be key to students intuitively understanding this concept. An alternative is to give students access to technology and have them do this in pairs or on their own. 
• The post, "Seeing Stars with Random Sampling" on MathCoachBlog is a great resource for understanding and finding some good activities/understanding on these topics.
• Sample Size Calculator by Creative Research Systems is a good calculator for sample size that you can use to gauge student understanding of sample size.
• This lesson borders on the “central limit theorem” through Anchor Problem #2. You do not need to give the students this language.

Below are three dot plots of the proportion of tails in 20, 60, or 120 simulated slips of a coin. The mean and standard deviation of the sample proportions are also shown for each of the three dot plots. Match each dot plot with the appropriate number of flips. Clearly explain how you matched the plots with the number of simulated flips.