Section 5A

Section 5A

Fundamentals of Statistics

Open Ended

15 –20: Population and Sample. For the following studies, identify the population, sample, population parameters, and sample statistics.

15. In order to gauge public opinion on the President’s plan to contain Iran’s nuclear program, the Pew Research Center surveyed 1001 Americans by telephone.

Open Ended

15 –20: Population and Sample. For the following studies, identify the population, sample, population parameters, and sample statistics.

17. Astronomers typically determine the distance to a galaxy (a huge collection of billions of stars) by measuring the distances to just a few stars within it and taking the mean (average) of these distance measurements.

Open Ended

21. You want to determine what percentage of high school ­seniors regularly use a cell phone while driving.

Basic Steps in a Statistical Study

1. State the goals of your study. That is, determine the population you want to study and exactly what you’d like to learn about it.

2. Choose a representative sample from the population.

3. Collect raw data from the sample and summarize these data by finding sample statistics of interest.

4. Use the sample statistics to infer the population parameters.

5. Draw conclusions: Determine what you learned and how it addresses your goals.

Open Ended

27. Representative Sample? You want to determine the average number of classes skipped by first-year students at a small college during a particular semester. State whether each of the following samples is likely to be representative and ­explain why or why not.

Sample 1: 100 first-year students who belong to a sorority or fraternity.

Sample 2: 100 first-year students who play a varsity sport.

Sample 3: The first 100 first-year students whom you meet at the student union.

Sample 4: 100 first-year students taking honors humanities courses

Multiple Choice

29 –34: Identify the Sampling Method. Identify the sampling method (simple random sampling, systematic sampling, convenience sampling, or stratified sampling) in the following studies.

31. A study of the use of antidepressants selects 50 participants between the ages of 20 and 29, 50 participants between the ages of 30 and 39, and 50 participants between the ages of 40 and 49.

• simple random sampling

• systematic sampling

• convenience sampling

• stratified sampling

Multiple Choice

29 –34: Identify the Sampling Method. Identify the sampling method (simple random sampling, systematic sampling, convenience sampling, or stratified sampling) in the following studies.

32. Every 100th cast iron pipe that comes off an assembly line is tested for strength.

• simple random sampling

• systematic sampling

• convenience sampling

• stratified sampling

Multiple Choice

29 –34: Identify the Sampling Method. Identify the sampling method (simple random sampling, systematic sampling, convenience sampling, or stratified sampling) in the following studies.

33. Student ID numbers are randomly selected by a computer for a survey of student opinions on college athletics.

• simple random sampling

• systematic sampling

• convenience sampling

• stratified sampling

Multiple Choice

35 –40: Type of Study. Determine whether each of the following studies described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.

35. A study at the University of Southern California separated 108 volunteers into groups, based on psychological tests ­designed to determine how often they lied and cheated. Those with a tendency to lie had different brain structures than those who did not lie (British Journal of Psychiatry).

• observational

• experiment

Multiple Choice

35 –40: Type of Study. Determine whether each of the following studies described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.

35. A study at the University of Southern California separated 108 volunteers into groups, based on psychological tests ­designed to determine how often they lied and cheated. Those with a tendency to lie had different brain structures than those who did not lie (British Journal of Psychiatry).

• retrospective

• not retrospective

Open Ended

35 –40: Type of Study. Determine whether each of the following studies described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.

35. A study at the University of Southern California separated 108 volunteers into groups, based on psychological tests ­designed to determine how often they lied and cheated. Those with a tendency to lie had different brain structures than those who did not lie (British Journal of Psychiatry).

Case and control groups?

Multiple Choice

35 –40: Type of Study. Determine whether each of the following studies described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.

38. In a study of the effects of magnets on back pain, some subjects were treated with magnets while others were given non-magnetic devices with a similar appearance (Journal of the American Medical Association). (The magnets did not appear to be effective in treating back pain.)

• observational

• experimental

Open Ended

35 –40: Type of Study. Determine whether each of the following studies described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.

38. In a study of the effects of magnets on back pain, some subjects were treated with magnets while others were given non-magnetic devices with a similar appearance (Journal of the American Medical Association). (The magnets did not appear to be effective in treating back pain.)

control and treatment groups? single or double blind?

Multiple Choice

35 –40: Type of Study. Determine whether each of the following studies described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.

39. A study by Brown University social scientists found that 18.6% of first-year women students surveyed at an upstate New York college experienced sexual assault during that first year (Journal of Adolescent Health).

• observational

• experiment

Multiple Choice

35 –40: Type of Study. Determine whether each of the following studies described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.

39. A study by Brown University social scientists found that 18.6% of first-year women students surveyed at an upstate New York college experienced sexual assault during that first year (Journal of Adolescent Health).

• retrospective

• not retrospective

Open Ended

41 –46: What Type of Study? What type of statistical study is most likely to lead to an answer to the following questions? If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.

45. Does taking a daily multivitamin reduce the incidence of strokes?

Open Ended

47 –50: Margin of Error. The following summaries of statistical ­studies give a sample statistic and a margin of error. Find the confidence ­interval and answer any additional questions.

47. A poll is conducted the day before an election for state senator. There are two candidates running. The poll shows that 53% of the voters surveyed favor the Republican candidate, with a margin of error of 2.5 percentage points. Should the Republican be confident that she’ll have a victory party? Why or why not?

Open Ended

52 –57: Real Studies. Consider the following statistical studies.

53. A Fox News poll of 900 registered voters found that 19% of Americans “regift” (give gifts that they received as gifts). Women (21%) are more likely to regift than men (16%), and the results are nearly independent of income. The margin of error was 3 percentage points.

a. Identify the population and the population parameter of interest.

Open Ended

52 –57: Real Studies. Consider the following statistical studies.

53. A Fox News poll of 900 registered voters found that 19% of Americans “regift” (give gifts that they received as gifts). Women (21%) are more likely to regift than men (16%), and the results are nearly independent of income. The margin of error was 3 percentage points.

b. Describe the sample and sample statistic for the study.

Open Ended

52 –57: Real Studies. Consider the following statistical studies.

53. A Fox News poll of 900 registered voters found that 19% of Americans “regift” (give gifts that they received as gifts). Women (21%) are more likely to regift than men (16%), and the results are nearly independent of income. The margin of error was 3 percentage points.

c. Identify the type of study.

Open Ended

52 –57: Real Studies. Consider the following statistical studies.

53. A Fox News poll of 900 registered voters found that 19% of Americans “regift” (give gifts that they received as gifts). Women (21%) are more likely to regift than men (16%), and the results are nearly independent of income. The margin of error was 3 percentage points.

d. Discuss what additional facts you would like to know before you believed the study or acted on the results of the study.

Open Ended

52 –57: Real Studies. Consider the following statistical studies.

54. The phenomenon of stereotype threat occurs when people, often women or minorities, are reminded before taking a test that the test will be used to evaluate intellectual or academic abilities. Studies show that test performance declines significantly when such reminders are given compared to performance when they are not given (Psychological Science, 15, 829–836).

a. Identify the population and the population parameter of interest.

Open Ended

52 –57: Real Studies. Consider the following statistical studies.

54. The phenomenon of stereotype threat occurs when people, often women or minorities, are reminded before taking a test that the test will be used to evaluate intellectual or academic abilities. Studies show that test performance declines significantly when such reminders are given compared to performance when they are not given (Psychological Science, 15, 829–836).

b. Describe the sample and sample statistic for the study.

Open Ended

52 –57: Real Studies. Consider the following statistical studies.

54. The phenomenon of stereotype threat occurs when people, often women or minorities, are reminded before taking a test that the test will be used to evaluate intellectual or academic abilities. Studies show that test performance declines significantly when such reminders are given compared to performance when they are not given (Psychological Science, 15, 829–836).

c. Identify the type of study.

Open Ended

52 –57: Real Studies. Consider the following statistical studies.

54. The phenomenon of stereotype threat occurs when people, often women or minorities, are reminded before taking a test that the test will be used to evaluate intellectual or academic abilities. Studies show that test performance declines significantly when such reminders are given compared to performance when they are not given (Psychological Science, 15, 829–836).

d. Discuss what additional facts you would like to know before you believed the study or acted on the results of the study.