This activity illustrates how sampling bias can result when you use a nonrandom sample, even if you attempt to make it representative: You are in a geography class, discussing center and variability for several characteristics of the states in the contiguous United States. A particular value of center is the mean area of the states. A map and a list of the states with their areas (in square miles) are shown in the figure and table that follow. Area for a state includes dry land and permanent inland water surface. Although we could use these data to calculate the actual mean area, let?s explore how well sampling performs in estimating the mean area by sampling five states and finding the sample mean.a. The most convenient sampling design is to use our eyes to pick five states from the map that we think have areas representative of all the states. Do this, picking five states that you believe have areas representative of the actual mean area of the states. Compute their sample mean area.b. Collect the sample means for all class members. Construct a dot plot of these means. Describe the distribution of sample means. Note the shape, center, and variability of the distribution.c. Another possible sampling design is simple random sampling. Randomly select five states (using an app or computer program) and compute the samplemean area.d. Collect the sample means from part c of all class members. Construct a dot plot of the sample means using the same horizontal scale as in part b. Describe this distribution of sample means. Note the shape, center, and variability of the distribution.e. The true mean total land area for the 48 states can be calculated from the accompanying table by dividing the total at the bottom of the table by 48. Which sampling method, using your eyes or using random selection, tended to be better at estimating the true population mean? Which method seems to be less biased? Explain.f. Write a short summary comparing the two distributions of sample means.

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Areas of the 48 States in the Continental U.S. State Area (square mil Alabama 52,419 113,998 53,179 163,696 104,094 5,543 2,489 65,755 59,425 83,570 57,914 36,418 56,272 82,277 40,409 51,840 35,385 12,407 10,555 96,716 86,939 48,430 69,704 147,042 77,354 110,561 9,350 8,721 121,589 54,556 53,819 70,700 Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota