Lesson 3.3 – Simple Random Samples

  • Describe how to obtain a simple random sample using slips or paper or technology.
  • Explain the concept of sampling variability and the effect of increasing sample size.
  • Use simulation to test a claim about a population proportion.

 

Activity: Gettysburg Address Part 2 

Photo Oct 26, 10 49 31 AM
n = 5

Students worked in pairs on the Activity.  The purpose of the Activity is to see what happens to the sampling distribution from yesterday when we increase the sample size from 5 to 10.  The results are pictured at right.

As a class, we had a discussion about how we could compare the distribution with n = 5 to the distribution with n = 10 (shape, center, variability, and outliers).  The biggest difference is that the variability decreases.  To help students understand why this might happen, we started by pointing to the 6.2 estimate when n = 5 (the largest estimate).

Photo Oct 28, 5 28 30 AM
n = 10

“How could this happen?”  Maybe we just had one outlier word of length 11 that brought the average up to 6.2.  “Would this be more or less likely to happen with a sample of size 10?”  Less likely as there would be 9 other values to bring the average back down.  With a higher sample size, it is less likely that we will get averages that are farther away from the true mean.

 

Notes

When discussing how to use technology to select a simple random sample, we made sure that students discussed (1) Labeling each word with a number, (2) using a calculator (or Siri) to get a random number between 1 and 268 with no repeats, and (3) select five words.

When discussing how to use slips of paper to select a simple random sample, we made sure that students discussed (1) writing each word onto slips of identical sized paper, (2) put papers into a hat and mix well, and (3) select 5 pieces of paper and use the words on these slips.

 

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