Access the Sampling Distribution of the Sample Mean (discrete variable) web app on the book’s website. Enter the probabilities P1X = x2 of 0.1667 for the numbers 1 through 6 to specify the probability distribution of a fair die. (This is a discrete version of the uniform distribution shown in the first column of Figure 7.11.) The resulting population distribution has μ = 3.5 and σ = 1.71.
a. In the box for the sample size n, enter 2 to simulate rolling two dice. Then, press the Draw Sample(s) button several times and observe how the histogram for the simulated sampling distribution for the mean number shown on two rolls is building up. Finally, simulate rolling two dice and finding their average 10,000 times by selecting the corresponding option. Describe (shape, center, spread) the resulting simulated sampling distribution of the sample mean, using the histogram of the 10,000 generated sample means. (Note: Statistics for the simulated sampling distribution are reported in the tile of its plot.)
b. Are the reported mean and standard deviation of the simulated sampling distribution close to the theoretical mean and standard deviation for this sampling distribution? Compute the theoretical values and compare.
c. Repeat part a, but now simulate rolling n = 30 dice an finding their average face value. What are the major changes you observe in the simulated sampling distribution?