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Application

Now that you have completed all of the activities in this chapter, use the concepts and techniques that you've learned to respond to these questions.

  1. Scenario: You live in a community of 23,847 households. You want to select a simple random sample of 250 of these households from a printed list of addresses.

    1. Use JMP to generate a random list of 250 integers; report the first 10 and last 10 integers on the list.

    2. Suppose that, from prior figures, you estimate that 18% of these households (approximately 4,300) have no Internet service. Use what you've learned in this chapter to estimate the probability that a random sample of 250 households would contain only households with Internet service.

    3. Estimate the probability that an SRS of 250 households would include 25 or fewer homes without Internet service.

    4. Is there any realistic chance that an SRS of 250 households would be made up entirely of homes without Internet service? Explain your thinking.

  2. Scenario: Recall the World Development Indicators data in BirthRate 2005.

    1. First, analyze the full table to determine the actual proportion of all countries that are in Sub-Saharan Africa. What is that proportion?

    2. Now find and report the mean and standard deviation of the infant mortality rate for all countries.

    3. Select a random sample of 30 countries. In your sample, what was the proportion of Sub-Saharan African countries? What was the mean infant mortality rate? How do your sample statistics compare to the values that you found in parts a and b? In your own words, explain the discrepancies.

  3. Scenario: You want to develop a deeper understanding of sampling variability for categorical data by making further use of the Samp_Dist_SampProp simulator script. We'll imagine that you want to conduct a large-scale survey to learn what proportion of the population favors a particular issue. Complete the following activities, and report briefly on what you find.

    1. Set the population characteristics as follows: the Population Proportion is 0.4, and the sample size is 1,000. Set the Category Name to Favor.

      Generate 5,000 samples by repeatedly running the simulation and describe the distribution of sample proportions.

    2. Reset the simulator, and keep the population proportion set at 0.4, but change the sample size to 250. Again generate 5,000 simulated samples and report on what you find. If we reduce the sample size by a factor of ¼, what happens to the center, shape, and spread of the sampling distribution?

    3. Reset once again, and change the population proportion to 0.95, keeping the sample size at 250. Generate 5,000 samples, and compare your results to those obtained in part b.

    4. In major public opinion polls, pollsters often choose sample sizes around 250 or around 1,000. What difference does the size of the sample make?

    5. If you were conducting an important public opinion survey and were concerned about the potential adverse impacts of sampling variation, would you be better off sampling from a population in which there was considerable uniformity (say, in which 95% of the population agreed on an issue) or a population that was split on the issue? Explain how this exercise shapes your response.

  4. Scenario: You want to develop a deeper understanding of sampling variability for continuous data by making further use of the Samp_Dist_SampMean simulator script. In this scenario, you are investigating the number of seconds required for a particular Web site to respond after a user issues a request. Complete the following activities, and report briefly on what you find.

    1. Set the population characteristics as follows: the Population Shape is Normal, the Population Mean is 15 seconds, the Standard Deviation is 3.3 seconds, and the Name of the Variable is Response Time. The Sample Size is 1,000. Generate 10,000 samples, and describe the distribution of sample means.

    2. Reset the simulator, and keep the other settings the same as in part a, but change the sample size to 250. Again, generate 10,000 simulated samples, and report on what you find. If we reduce the sample size by a factor of ¼, what happens to the center, shape, and spread of the sampling distribution?

    3. Reset once again, and change the population standard deviation to 6.6 seconds, keeping the sample size at 250. Generate 10,000 samples, and compare your results to those obtained in part b.

    4. Now reset the simulator, change the Population Shape to Right-Skewed, and repeat the other settings from part a. How do your results compare to those obtained in part a?

    5. Once again, reset and change the Population Shape to Uniform to model a population in which all values have the same probability.

    6. In the prior questions, we've varied the shape of the parent population, the size of our samples, and the amount of variability within the population (standard deviation). Write a few sentences summarizing how each of these changes impacts the nature of sampling variability.


  

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