RANDOM FORTUNES: PART I


SCENARIO

Results from polls and other statistical studies reported in a newspaper or magazines often emphasize the point that the samples were randomly selected. Why the emphasis on randomization? Couldn't a good investigator do better by carefully choosing respondents to a poll so that various interest groups were represented? Perhaps, but samples selected without objective randomization tend to favor one part of the population over another. For example, polls conducted by sports writers tend to favor the opinions of sport fans. This leaning toward one side of the issue is called sampling bias. In the long run, random samples seem to do a good job of producing samples that fairly represent the population. In other words, randomization reduces sampling bias.

QUESTION

How do random samples compare to subjective samples in terms of sampling bias?

OBJECTIVES

Subjective (or judgmental) samples will be compared to random samples in terms of sampling bias. The goal is to learn why randomization is an important part of data collection.

ACTIVITY

1. JUDGMENTAL SAMPLES
a. Click on the $1 coin to look at the figure which shows fortunes of 100 "very rich" people for a few seconds and write down your guess as to the average fortune in the following box. For example, the fortune of the person number 25 is $19.

Logon:
Password:

INITIAL GUESS

b. Click on the $1 coin to select 5 persons that, in your judgment, are representative of the people on the figure. Write down the fortune for each of the five.

FORTUNE

Compute the average of the five fortunes and compare it to your guess.

EYEBALL (Average)

Are they close?

2. RANDOM SAMPLES

a. Use a random number table or a random number generator in a computer or calculator to select 5 distinct random numbers between 00 and 99. Find 5 people with these numbers, using 00 to represent person number 100, and mark them on the sheet. This is your random sample of 5 fortunes.


By Using of Random Number Table: Enter the table of random numbers anywhere and read two-digit numbers. Suppose we enter at line 3, which is

30734 71571 83722 79712 25775 65178 07763 82928 31131 30196

The first 5 two-digit groups are

30 73 47 15 71

Therefore, your sample will consist of fortunes 30, 73, 47, 15, and 71.

Click on the following box to reach to a table of random numbers.



By Using MINITAB: Run MINITAB and type the following commands.

MTB> Random 5 C1;

SUBC> Integer 0 to 99.

MTB> Print C1


b. Write down the fortunes of these 5 sampled fortunes and find the average.

FORTUNE
AVERAGE

How does the average of the random sample compare with your guess? How does it compare with your average for the subjective sample?

The instructor will collect the averages from the subjective and random samples and ask you to continue to do this activity in Part II.