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Psyc 200 Statistics: An Activity-Based Approach
H.M. Sinnamon
Assignment 4
General instructions:
Type “This is my own work” and your name at the end.
Random sampling exercise
Based on exercises 4.8 and 4.9 in text.
This exercise will show how the law of large numbers operates when random samples are drawn from a population.
Suppose in the population of married women, a proportion of .73 believe that their husbands do his fair share of
work around the house.
Use Minitab to simulate this population and to draw samples from it.
A. Calc, Random data, Bernouli,
500 rows of data, store in C1, probability of success = .73
Label C1 “population” .
B. Take random samples of size 20, 80 and 320 from the population.
Label C2 “20sample”, C3: “80sample”, C4: “320sample”
Calc, random data, sample from columns
20 rows, from population, store in 20sample
80 rows, from population, store in 80sample
320 rows, from population, store in 320sample
1. You now have 3 random samples of different sizes. State the means and compare them to the
population. Note that the population mean will probably not be precisely .73. Which sample has a mean
closest to the population? Do your data conform to the law of large numbers?
C. Look at the pattern when repeated samples of small and large sizes are drawn.
You will draw 10 samples of size 20 and 10 samples of size 320. Minitab will do this easily,
Label two new columns “n20x10” and “n320x10”
Calc, random data, binomial
10 rows, store in n20x10, 20 trials, probability of success .73
10 rows, store in n320x10, 320 trials, probability of success .73
You have two columns with the number of success in each of 10 samples of either size 20 or 320.
Use the calculator to compute the proportions for the two columns. Store them in two new columns; label the
columns appropriately so you do not have to remember which is which.
2. Compare the means and standard deviations of the distributions of the two sample sizes.
Which sample size has a distribution with a mean closest to the population mean.
Which sample size has a distribution with the least variability.
Exercises from text:
No illustrations are necessary, just give the numbers.
4.14
4.18