Introduction to Statistics — practice test 1B

aleX21267

Nov 29, 2016

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

Provide an appropriate response.
- 1. Define sampling error and nonsampling error. Give examples of nonsampling error.
  
  Possible answer
  Sampling error is the difference between a sample result and the true population result. Such an error results from chance sample fluctuations. A nonsampling error occurs when the sample data are incorrectly collected, recorded, or analyzed. Examples include nonrandom samples, defective measuring instruments, biased survey questions, a large number of refusals, copying sample data incorrectly.
Determine whether the given value is a statistic or a parameter.
- 2. After inspecting all of 55,000 kg of meat stored at the Wurst Sausage Company, it was found that 45, 000 kg of the meat was spoiled.
  1. Parameter
  2. Statistic
Identify the number as either continuous or discrete.
- 3. The number of stories in a Manhattan building is 22.
  1. Discrete
  2. Continuous
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
- 4. Student’s grades, A, B, C, on a test.
  1. Nominal
  2. Ordinal
  3. Interval
  4. Ratio
- 5. Ages of survey respondents.
  1. Nominal
  2. Ordinal
  3. Interval
  4. Ratio
Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.
- 6. In a poll of 50,000 randomly selected college students, 74% answered “yes” when asked “Do you have a television in your dorm room?”
  1. Not representative
  2. Population: the 50,000 selected college students
  3. Population: all college students
  4. Sample: all college students
  5. Representative
  6. Sample: the 50,000 selected college students
Use critical thinking to develop an alternative conclusion.
- 7. A study shows that adults who work at their desk all day weigh more than those who do not. Conclusion: Desk jobs cause people to gain weight.
  
  Possible answer
  Desk job workers are confined to their chairs for most of their work day. Other jobs require standing or walking around which burns calories. It is probably the lack of exercise that causes higher weights, not the desk job itself. Avoid causality altogether by saying lack of walking and exercise is associated with higher weights.
Use critical thinking to address the key issue.
- 8. You plan to make a survey of 200 people. The plan is to talk to every 10^th person coming out of the school library. Is there a problem with your plan?
  
  Possible answer
  People who don’t go to the library are excluded.
- 9. A questionnaire is sent to 10,000 persons. 5,000 responded to the questionnaire. 3,000 of the respondents say that they “love chocolate ice cream”. We conclude that 60% of people love chocolate ice cream. 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.
Perform the requested conversions. Round decimals to the nearest thousandth and percents to the nearest tenth of a percent, if necessary.
- 10. Convert 90% to an equivalent fraction and decimal.
  1. ⁴/₅, 9
  2. ⁴/₅, 0.9
  3. ⁹/₁₀, 9
  4. ⁹/₁₀, 0.9
- 11. Convert ¹⁷/₁₅₀ to an equivalent decimal and percent.
  1. 0.113, 1.13%
  2. 0.233, 23.3%
  3. 0.113, 11.3%
  4. 0.233, 233%
Solve the problem.
- 12. On a test, if 80 questions are answered and 36% of them are correct, what is the number of correct answers?
  1. 32
  2. 45
  3. 50
  4. 29
Is the description an observational study or an experiment?
- 13. A quality control specialist compares the output from a machine with a new lubricant to the output of machines with the old lubricant.
  1. Observational study
  2. Experiment
- 14. A stock analyst select a stock from a group of twenty for investment by choosing the stock with the greatest earnings per share reported for the last quarter.
  1. Observational study
  2. Experiment
Identify the type of observational study.
- 15. A statistical analyst obtains data about ankle injuries by examining a hospital’s records from the past 3 years.
  1. Prospective
  2. Retrospective
  3. None of these
  4. Cross-sectional
Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience.
- 16. A market researcher selects 500 drivers under 30 years of age and 500 drivers over 30 years of age.
  1. Cluster
  2. Stratified
  3. Random
  4. Convenience
  5. Systematic
- 17. A market researcher selects 500 people from each of 10 cities.
  1. Random
  2. Systematic
  3. Convenience
  4. Stratified
  5. Cluster
- 18. An education researcher randomly selects 48 middle schools and interviews all the teachers at each school.
  1. Convenience
  2. Cluster
  3. Stratified
  4. Systematic
  5. Random
Provide an appropriate response.
- 19. A researcher obtains a sample of high school teachers in his school district by randomly selecting 10 high schools and interviewing all the teacher at each of these 10 schools. What kind of sampling is being used here? Will the resulting sample be a simple random sample of the population of teachers in the school district? Explain your thinking.
  
  Possible answer
  This is cluster sampling. The sample obtained will not be a simple ransom sample of all high school teachers in the district because different samples have different chances of being selected.
  
  20. Why do you think that cluster sampling is frequently used in practice?
- Possible answer
  Answers will vary. Possible answer: Cluster sampling can save time and money and be more efficient, especially when the clusters are geographically far apart from each other. For example, if a researcher wishes to interview a sample of high school teachers in a school district, it will be easier to interview all the teachers at a few schools than to interview a few teachers from many different schools.

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