Nov 29, 2016

Introduction to Statistics — practice test 1A

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

  • Provide an appropriate response.
    • 1. Define random sample. Explain why this is important in design of experiments.

      Possible answer
      In random sampling, each member of the population has an equal chance of being selected. Random sampling provides us with the best representative sample in which all groups of the population are approximately proportionately represented. Careless sampling can easily result in a biased sample which may be useless.

    • Determine whether the given value is a statistic or a parameter.
      • 2. A sample of 120 employees of a company is selected, and the average age is found to be 37 years.
        1. Parameter
        2. Statistic

    • Identify the number as either continuous or discrete.
      • 3. The number of freshmen entering college in a certain year is 621.
        1. Continuous
        2. Discrete

    • Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
      • 4. Survey responses of “good, better, best”.
        1. Nominal
        2. Interval
        3. Ordinal
        4. Ratio

      • 5. Salaries of college professors.
        1. Ratio
        2. Interval
        3. Ordinal
        4. Nominal

    • Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.
      • 6. An employee at the local ice cream parlor asks three customers if they like chocolate ice cream.
        1. Sample: the 3 selected customers
        2. Population: all customers
        3. Representative
        4. Sample: all customers
        5. Population: the 3 selected customers
        6. Not representative

    • Use critical thinking to develop an alternative conclusion.
      • 7. In a study of headache patients, every one of the study subjects with a headache was found to be improved after taking a week off of work. Conclusion: taking time off work cure headaches.

        Possible answer
        Headaches generally last for only a few hours, so anything would seem like a cure. There is no evidence to suggest that taking time off work will cure a headache.

      • Use critical thinking to address the key issue.
        • 8. An airline company advertises that 100% of their flights are on time after checking 5 randomly selected flights and finding that these 5 were on time.

          Possible answer
          The sample was too small.

          1. 9. “38% of adults in the United States regularly visit a doctor”. This conclusion was reached by a college student after she had questioned 520 randomly selected members of her college. What is wrong with her survey?

            Possible answer
            The sample is biased. College students are not representative of the U.S. population as a whole.

          2. Perform the requested conversions. Round decimals to the nearest thousandth and percent to the nearest tenth of a percent, if necessary.
            • 10. Convert 0.4 to an equivalent fraction and percentage.
              1. 3/10, 4%
              2. 3/10, 40%
              3. 2/5, 40%
              4. 2/5, 4%

            • 11. Convert 90% to an equivalent fraction and decimal.
              1. 9/10, 9
              2. 4/5, 0.9
              3. 9/10, 0.9
              4. 4/5, 9

          3. Solve the problem.
            • 12. On a test, if 125 questions are answered and 68% of them are correct, what is the number of correct answers?
              1. 90
              2. 85
              3. 62
              4. 54

          4. Is the description an observational study or an experiment?
            • 13. A stock analyst compares the relationship between stock prices and earnings per share to help him select a stock for investment.
              1. Observational study
              2. Experiment

            • 14. A TV show’s executives raised the fee for commercials following a report that the show received a “No. 1” rating in a survey of viewers.
              1. Experiment
              2. Observational study

          5. Identify the type of observational study.
            • 15. A town obtains current employment data by polling 10,000 of its citizens this month.
              1. Prospective
              2. None of these
              3. Cross-sectional
              4. Retrospective

          6. Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience.
            • 16. 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.
              1. Systematic
              2. Stratified
              3. Cluster
              4. Convenience

            • 17. A sample consists of every 49th student from a group of 496 students.
              1. Convenience
              2. Systematic
              3. Cluster
              4. Stratified

            • 18. The name of each contestant is written on a separate card, the cards are placed in a bag, and three names are picked from the bag.
              1. Systematic
              2. Convenience
              3. Random
              4. Cluster
              5. Stratified

          7. Provide an appropriate response.
            • 19. Explain what is meant by the term “confounding” and give an example of an experiment in which confounding is likely to be a problem.

              Possible answer
              Confounding occurs in an experiment when the effects of two or more variables cannot be distinguished from each other. Examples will vary.

              One example is that of a school district that conducts a study regarding whether the science laboratory approach or the computer simulation approach is better for learning chemistry among seniors. One school is randomly selected to conduct only science labs; the other, only computer simulations. A standardized achievement test is used to measure learning, and the results of the two schools are compared. Unless controlled in the study, two confounding variables are teaching expertise and student motivation.

              1. 20. A researcher wants to obtain a sample of 100 school teachers from the 800 school teachers in a school district. Describe procedures for obtaining a sample of each type: random, systematic, convenience, stratified, cluster.

                Possible answer
                Answers will vary.
                One answer is as follows.
                (1) Random: List the names of the teachers in alphabetical order from 1 through 800. Select 100 teacher by a random number computer program.

                (2) Systematic: Blindly select from a box one of eight index cards, each of which has a number from 1 to 8 written on it. Sample from the alphabetized list, beginning with that number followed by all its integral multiples until 100 teachers are selected.

                (3) Convenience: Offer an incentive to the teachers, and select the first 100 volunteers.

                (4) Stratified: Prepare an alphabetized list of teachers by school (i.e., strata) and randomly select teachers in proportion to school size until 100 teachers are selected.

                (5) Cluster: Form 8 clusters from 8 consecutive blocks of 100 teachers in the alphabetized list. Blindly draw an index card from the box, and whichever card is drawn, all 100 teachers in than cluster will be the sample. Making clusters from the individual schools might not work, since the school or schools randomly selected might not have 100 teachers in total.

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