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Section1.3Chapter 1 Exercises

  1. This year, Cunningham Lake in Omaha has been fighting an infestation of zebra mussels, an invasive species. Suppose that the Nebraska Game and Parks Commission wants to estimate their population. They capture and mark 194 zebra mussels, then release them back into the lake. After waiting a month, they capture 84 mussels, of which 13 had previously been marked. Using this data, estimate the number of zebra mussels in Cunningham Lake.
  2. The UNL Office of Global Strategies conducts its own experiment to find out how many students study abroad. They know that there are 26,000 students in total at UNL. They survey 700 randomly selected students, of whom 95 have studied abroad while at UNL. The surveys take place in person on campus.

    1. To use this data to approximate the total number of UNL students who have studied abroad, which enumeration method would we use: one sample estimation or mark-recapture?
    2. Use the method you chose in part (a) to compute an approximation of the number of students who have studied abroad.
    3. Identify the parameter and the statistic in this problem.
    4. Identify possible sources of sampling bias.
  3. Your class of Math 203 students decides to conduct a study to estimate the number of students at UNL who study abroad. You survey a random group of 75 students from among the current sections of Math 203, of whom 21 have studied abroad while at UNL.

    1. What is the target population in this experiment? What is the parameter (described in words)?
    2. Is the sample a random collection of students from the target population? Why or why not? (Use the definition of a random sample to explain.)
    3. Identify possible ways in which the outcome might be biased.
  4. For each of the following, indicate whether the study described is observational or experimental and how you know.

    1. Researchers ask students at a local high school about their grade point average and the typical amount of sleep they get each night. They examine data to determine whether their is a correlation between the grades and sleep.
    2. Researchers collected data to examine the relationship between air pollution and preterm births in an urban setting. They collect air pollution levels, length of gestation data and pollution exposure data before birth for all infants born in the city over a 5 year period.
    3. Researchers study the relationship between honesty, age, and self-control by asking child between ages 5 and 15 to toss a fair coin in private and record the outcome, only one of which would result in a reward. Half the students were explicitly told not to cheat and the others were not given any explicit instructions. Differences were observed in the cheating rates in the instruction and no instruction groups, as well as some differences across childrens characteristics within each group. (Adapted from "Advanced High School Statistics", by Diez et al.)
  5. A group of Math 203 students has been asked to find out which type of coffee is preferred by students at UNL: Starbucks, Scooter's, Dunkin Donuts or coffee from The Mill. Since it is not feasible to contact every UNL student, the group needs to gather information using only a sample of UNL students, so they decide to interview students as they exit the Learning Commons, at the entrance by Dunkin Donuts. Of the 124 students interviewed, 38 prefer Starbucks, 16 prefer Scooter's, 66 prefer Dunkin Donuts, and 4 prefer coffee from The Mill. Using this information, the group makes the claim that 31% of all UNL students prefer Starbucks, 13% prefer Scooter's, 53% prefer Dunkin Donuts, and 3% prefer coffee from The Mill.

    1. How did the group arrive at these percentages?
    2. What is the target population? What are the parameters? What are the statistics?
    3. What type of biased sampling method did the group use? How do you know?
    4. Do you believe the group's claim about UNL students is legitimate? Why or why not?
    5. Describe a simple random sampling method that would give a more accurate estimate of the preferred type of coffee among all UNL students.
  6. Identify the most relevant source of bias in this situation: A survey asks the question, Should the mall prohibit loud and annoying rock music in clothing stores catering to teenagers?
  7. Identify the most relevant source of bias in this situation: To determine opinions on voter support for a downtown renovation project, a surveyor randomly questions people working in downtown businesses.