**Homework 4: Probability and Sampling (8 points)**

A&A Ch 4: 1.delm, 2cd, 3ab

Sampling Problems: See table 4.2 in Knapp (p. 34), generated by taking 50 random samples of
size 4. He is looking at the percentage black.

1. Using the cards he drew, calculate the mean denomination for each sample, counting A=1,
J=11, Q=12, & K=13. So, for first sample, this would be mean of 10,5,13,10; for second sample,
mean of 1,12,12,1, and so on. Create a histogram for the sample means on SPSS, and calculate
the mean and standard deviation for this distribution.

2. Next, take 20 of your own random samples from a card deck (replacing cards after each draw)
but this time, use samples of 10 cards each. Calculate the mean denomination for each sample,
enter this into SPSS, create a histogram for the sample means, and calculate mean and standard
deviation for this distribution.

3. Discuss the results. How close are these sample means, on average, to the true population
mean for denomination, which is 7? Which set of means deviate more, on average, from the true
mean? Why? Also discuss the differences in the frequency distributions of these sample means
from the distribution of denomination in the population (which is rectangular).