A sampling experiment. Figures 3.11 and 3.12 show how the sample proportion p behaves when we take many samples from a population in which the

A sampling experiment. Figures 3.11 and 3.12 show how the sample proportion ˆp behaves when we take many samples from a population in which the population proportion is p = 0.6. You can follow the steps in this process on a small scale.

Figure 3.16 is a small population. Each circle represents an adult. The white circles are people who ate in a restaurant last week, and the colored circles are people who did not.

You can check that 60 of the 100 circles are white, so in this population the proportion who ate in a restaurant last week is p = 60/100 = 0.6.

(a) The circles are labeled 00, 01, . . . , 99. Use line 111 of Table B to draw an SRS of size 5. What is the proportion ˆp of the people in your sample who ate in a restaurant last week?

(b) Take 9 more SRSs of size 5 (10 in all), using lines 122 to 130 of Table B, a different line for each sample. You now have 10 values of the sample proportion ˆp.

(c) Because your samples have only 5 people, the only values

ˆp can take are 0/5, 1/5, 2/5, 3/5, 4/5, and 5/5. That is, ˆp is always 0, 0.2, 0.4, 0.6, 0.8, or 1. Mark these numbers on a line and make a histogram of your 10 results by putting a bar above each number to show how many samples had that outcome.

(d) Taking samples of size 5 from a population of size 100 is not a practical setting, but let’s look at your results anyway. How many of your 10 samples estimated the population proportion p = 0.6 exactly correctly? Is the true value 0.6 roughly in the center of your sample values? Explain why 0.6 would be in the center of the sample values if you took a large number of samples.