Using a physical device to generate random samples. Using a die, generate a sample and evaluate the statistic. Then repeat many times and obtain an estimate of the sampling distribution. In particular, investigate the sampling distribution of the median for a sample of size 3 from the population distribution.
X f(x)
1............. 2/6
2............. 3/6
4............. 1/6
(a) Roll the die. Assign X = 1 if 1 or 2 dots show. Complete the assignment of values so that X has the population distribution when the die is fair.
(b) Roll the die two more times and obtain the median of the three observed values of X.
(c) Repeat to obtain a total of 25 samples of size 3. Calculate the relative frequencies, among the 75 values, of 1, 2, and 4. Compare with the population probabilities and explain why they should be close.
(d) Obtain the 25 values of the sample median and create a frequency table. Explain how the distribution in this table approximates the actual sampling distribution. It is easy to see how this approach extends to any sample size.