Applet Exercise Refer to Exercise 7.1. Use the applet DiceSample and scroll down to the

Chapter 7, Problem 7.3

(choose chapter or problem)

Applet Exercise Refer to Exercise 7.1. Use the applet DiceSample and scroll down to the next part of the screen that corresponds to taking samples of size n = 12 from the population corresponding to tossing a balanced die. a Take a single sample of size n = 12 by clicking the button Roll One Set. Use the button Roll One Set to generate nine more values of the sample mean. How does the histogram of observed values of the sample mean compare to the histogram observed in Exercise 7.1(c) that was based on ten samples each of size 3? b Use the button Roll 10 Sets nine more times until you have obtained and plotted 100 realized values (each based on a sample of size n = 12) for the sample mean Y . Click on the button Show Stats to see the mean and standard deviation of the 100 values (y1, y2,..., y100) that you observed. i How does the average of these 100 values of yi,i = 1, 2,..., 100 compare to the average of the 100 values (based on samples of size n = 3) that you obtained in Exercise 7.1(d)? ii Divide the standard deviation of the 100 values of yi,i = 1, 2,..., 100 based on samples of size 12 that you just obtained by the standard deviation of the 100 values (based on samples of size n = 3) that you obtained in Exercise 7.1. Why do you expect to get a value close to 1/2? [Hint: V(Y ) = 2/n.] c Click on the button Toggle Normal. The (green) continuous density function plotted over the histogram is that of a normal random variable with mean and standard deviation equal to the mean and standard deviation of the 100 values, (y1, y2,..., y100), plotted on the histogram. Does this normal distribution appear to reasonably approximate the distribution described by the histogram?