One of the key ideas in Section 2.2 was that the standard deviation of sample means is estimated by σ/√n? , when the population is large enough. We consider a population to be large enough when the population is more than 20 times the sample size. In Exploration 2.2 you used the words in the Gettysburg Address as the population. There are only 268 words in that speech, so the population is not that large. In this exercise you will use the Sampling Words applet to investigate how population size affects the estimate for the standard deviation of the sample means. 

a. The standard deviation of the length of the words in the Gettysburg Address is 2.119 letters. If we take repeated samples of 30 words from the Gettysburg Address, what is the predicted value of the standard deviation of sample means? 

b. In the Sampling Words applet, change the Sample size to 30 and take at least 50,000 samples from the Gettysburg Address. How does your standard deviation of your sample means from the applet compare to your answer from part (a)? Why might it be a bit different? 

c. Click on the radio button above the population data that has ×40 next to it. This will make it so you can sample from 40 copies of the Gettysburg Address and that your population size is now 40 × 268 = 10,720. Now take at least 50,000 samples. How does your standard deviation of your sample means from the applet compare to your answer from part (a)? Did a larger population size help you get a standard deviation closer to what was predicted in part (a)?