b. Look at the averages from the random samples of size 5 and construct a stemplot or a dot plot. How does this plot compare with the plots of the guessed values and the averages from the subjective samples in terms of center? In terms of spread?

c. From the data the instructor has provided for the whole class, calculate the mean of the sample averages for the subjective samples and for the random samples. How do the centers of the distributions of means compare.

d. Calculate the standard deviation of the averages for the subjective and for the random samples. How do the spreads of the distributions of means compare?

e. Having studied two types of sampling, subjective and random, which method do you think is doing the better job? Why?

SAMPLING BIAS

The actual distribution of fortunes together with the numerical and graphical summaries are provided below:

FORTUNE	NUMBER OF CASES
1	24
2	2
3	1
4	12
5	9
6	8
8	7
9	3
10	5
11	3
12	12
14	2
16	6
17	2
18	1
19	3
TOTAL	100

NUMERICAL SUMMARY

Number of Cases	Minimum	Maximum	Mean	Variance	Standard Deviation
100	1	19	7.15	28.573	5.345

a. Does either of the plots have a center that is very close to the true average?

Yes No

b. Does either of the plots have a center that is larger than the true average?

Yes No

c. Which one of the plots shows higher variability?

Subjective Random

d. Discuss the concept of the bias in sampling and how it relates to the two sampling methods (subjective and random) you just used.

WRAP-UP

a. Discuss the difference between sampling bias and measurement bias. Give examples of statistical studies in which each is an important consideration. Are either of these biases reduced appreciably by increasing the sample size?

b. Find an article printed in the media that reflects sampling bias. Discuss how the sampling bias could have affected the conclusions reported in the article.

EXTENSIONS

A. Using the same sheet of fortunes as used in Part I, select 20 multiple random samples of 10 fortunes each and compute the average area for each sample.

Plot these averages and compare the plot to the one of the random samples of size 5 with regard to:

a. center b. spread c. shape

B. Obtain a map of your state that shows the county boundaries. Your job is to show the geography department how to select a random sample of counties for purposes of studying land use. How would you select the samples? What might cause bias in the sampling process?

ASSESSMENT

A. Suppose that you are asked to design a sampling plan to find out

a. percent of broken links on the Internet

b. average amount of time to download a page on Internet

c. average amount of memory per computer

Choose one of the items and discuss how you would obtain the data. Discuss importance of randomization and sampling bias in your data collection plan.