STA 352 Project #2

In this exercise we will simulate drawing many random samples to help understand from whence the "confidence" in confidence interval comes. A recent L.A. Times poll indicated that 51% of Americans think it is acceptable for the government to monitor internet communications to hunt for terrorists. Assume for the purposes of this exercise that the value 51% is indeed true. We would like to see what would happen if we tried to estimate this value based on a random sample of size n = 2000.
1. Using Excel or another software, generate the percent of those in a sample of size 2000 who think it is acceptable for the government to monitor internet communications 100 times (i.e., generate 100 sample proportions).
2. Create a relative frequency table for the 100 results.
3. Using the frequency table, find the smallest margin of error (ME) so that the interval

sample proportion +/- ME
contains the population proportion (0.51) for 95% (approximately) of all samples.
4. The formula following (7.5-1) on p.380 shows how to calculate the interval in (3) assuming a very large number of samples has been taken. The value you computed in part (3) is an estimate for the margin of error in this formula. How does your estimate compare to the value given by the formula?
 

Hint: In Excel, use Tools>Data Analysis>Random number generation. Use a binomial distribution with p = 0.51 and n = 2000. To create a relative frequency table, use the Tools>Data Analysis>Histogram. Specify the range of values (note, you will have to convert number of responses to percent), and the "bin". The bin lists the possible values for the responses. A bin column containing the values .460, .461, .462, . . ., .560 should be sufficient.