Nov 29, 2016

Introduction to Statistics — practice test 1C

20 cards
, 53 answers
    Directions:
    Give your answers to the short-answer items. Circle the correct answer for multiple-choice items.

  • Provide an appropriate response.
    • 1. Define observational study and experiment. Define the terms “treatment group” and “control group” as part of your answer.

      Possible answer
      In an observational study, we observe and measure specific characteristics, but we don’t attempt to manipulate or modify the subjects being studied. In an experiment we apply some treatment and then proceed to observe its effects on the subjects. In the experiment, the group receiving the treatment is called the treatment group. The control group is the group that is not given the treatment.

    • Determine whether the given value is a statistic or a parameter.
      • 2. After taking the first exam, 15 of the student dropped the class.
        1. Statistic
        2. Parameter

    • Identify the number as either continuous or discrete.
      • 3. The average height of all freshmen entering college in a certain year is 68.4 inches.
        1. Continuous
        2. Discrete

    • Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
      • 4. Nationalities of survey respondents.
        1. Ordinal
        2. Nominal
        3. Interval
        4. Ratio

      • 5. Temperatures of the ocean at various depths.
        1. Ratio
        2. Interval
        3. Nominal
        4. Ordinal

    • Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.
      • 6. 100,000 randomly selected adults were asked whether they drink at least 48 oz of water each day and only 45% said “yes”.
        1. Sample: the 100,000 selected adults
        2. Not representative
        3. Population: all adults
        4. Representative
        5. Sample: all adults
        6. Population: the 100,000 selected adults

    • Use critical thinking to develop an alternative conclusion.
      • 7. A study of achievement scores by sixth-grade students on a standardized math test showed the three top scorers were all gifted piano players. Conclusion: Playing the piano leads to mathematical achievement.

        Possible answer
        A sample of 3 among many student is not sufficient to conclude that playing the piano is conducive to math achievement. Student motivation and interest in math should be considered as factors.

      • Use critical thinking to address the key issue.
        • 8. A researcher published this survey result: “74% of people would be willing to spend 10 percent more for energy from a non-polluting source”. The survey question was announced on a national radio show and 1,200 listeners responded by calling in. What is wrong with this survey?

          Possible answer
          This is not a random sample. The survey is based on voluntary, self-selected responses and therefore has serious potential for bias.

          1. 9. A researcher wished to gauge public opinion on gun control. He randomly selected 1000 people from among registered voters and asked them the following question: “Do you believe that gun control laws which restrict the ability of Americans to protect their families should be eliminated?” Identify the abuse of statistics and suggest a way the researcher’s methods could be improved.

            Possible answer
            The question is loaded. A more neutral way to phrase the question would be, for example, “Do you believe that gun control laws should be strengthened, weakened, or left in their current form?”

          2. Perform the requested conversions. Round decimals to the nearest thousandth and percents to the nearest tenth of a percent, if necessary.
            • 10. Convert 0.328 to an equivalent fraction and percent.
              1. 41/125, 32.8
              2. 41/125, 3.28%
              3. 8/25, 3.28%
              4. 8/25, 32.8%

            • 11. Convert 2.75 to an equivalent fraction and percent.
              1. 23/4, 27.5%
              2. 2 1/2, 275%
              3. 2 ¾, 275%
              4. 21/2, 27.5%

          3. Solve the problem.
            • 12. Alex and Juana went on a 95-mile canoe trip with their class. On the first day they traveled 19 miles. What percent of the total distance did they canoe?
              1. 5%
              2. 0.2%
              3. 20%
              4. 500%

          4. Is the description an observational study or an experiment?
            • 13. A TV show’s executives commissioned a study to gauge the impact of the show’s rating on the sales of its advertisers.
              1. Observational study
              2. Experiment

            • 14. A doctor performs several diagnostic tests to determine the reason for a patient’s illness.
              1. Observational study
              2. Experiment

          5. Identify the type of observational study.
            • 15. Researchers collect data by interviewing athletes who have won Olympic gold medals from 1980 to 1992.
              1. None of these
              2. Retrospective
              3. Cross-sectional
              4. Prospective

          6. Identity which of these types of sampling is used: random, stratified, systematic, cluster, convenience.
            • 16. A tax auditor selects every 1000th income return that is received.
              1. Stratified
              2. Convenience
              3. Systematic
              4. Cluster
              5. Random

            • 17. A pollster uses a computer to generate 500 random numbers, then interviews the voters corresponding to those numbers.
              1. Systematic
              2. Stratified
              3. Convenience
              4. Random
              5. Cluster

            • 18. To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day.
              1. Systematic
              2. Cluster
              3. Convenience
              4. Random
              5. Stratified

          7. Provide an appropriate response.
            • 19. A market researcher obtains a sample of 50 people by standing outside a store and asking every 20th person who enters the store to fill out a survey until she has 50 people. What sampling method is being used here? Will the resulting sample be a random sample? Will it be a simple random sample? Explain your thinking.

              Possible answer
              This is systematic sampling. The sample obtained will be a ransom sample because everyone has the same chance of being chosen but will not be a simple random sample as different samples of 50 people have different chances of being chosen.
              Note: That the sample is random depends on the market researcher randomly selecting 20 as the starting point prior to research.

              1. 20. A teacher at a school obtains a sample of students by selecting a random sample of 20 students from each grade. What kind of sampling is being used here? Will the resulting sample be a simple random sample of the population of students at the school? Explain your thinking.

                Possible answer
                This is stratified sampling. The sample obtained will not be a simple random sample because different samples of students have different chances of being selected.

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