MAT 135, Discussion Questions for Module 1

1. What is the difference between a population and a sample?

2. A psychologist wants to know if adults with normal vision can be fooled by a certain optical illusion. She recruits 50 students from her PSY 120 class and finds that 42 of them are fooled by the illusion.

a. The population for this study is what?

b. The sample for this study is what?

3. What is the difference between a parameter and a statistic?

4. The student newspaper runs a weekly question that readers can answer online or by campus mail. One question was “Do you think the college is doing enough to provide student parking?” Of the 82 people who responded, 79% said “No.”

a. What is the parameter being measured in this study?

b. What is the statistic in this study?

5. What is the difference between a descriptive statistic and an inferential statistic?

6. Give five examples of qualitative data that you could collect from your coworkers.

7. Give five examples of quantitative data that you could collect about your students.

8. Give two examples of quantitative data that is discrete.

9. Give two examples of quantitative data that is continuous.

10. Give two examples of data that is nominal (level of measurement).

11. Give two examples of data that is ordinal (level of measurement).

12. Give two examples of quantitative data that is interval (level of measurement).

13. Give two examples of quantitative data that is ratio (level of measurement).

14. What is the difference between an observational study and an experimental study?

15. What is the difference between a sample and a sampling frame?

16. What is the key feature of a simple random sample?

17. How is cluster sampling different from stratified sampling?

18. Why does a convenience sample lead to biased results?

19. For each of the following variables, determine if they are: a) qualitative or quantitative, b) if it is quantitative, is it discrete or continuous, c) is the level of measurement nominal, ordinal, interval or ratio (give the highest level it could be).

i. Temperature in Fahrenheit

ii. Numbers on soccer players’ jerseys

iii. Hair colour

iv. GPA

v. Height of buildings

vi. Degrees on a compass needle

vii. Age

viii. Time spent running a maze

ix. Gender

x. Skin cancer risk

20. What is the purpose of an institutional review board?

21. Give an example of a source of a study that would be considered

a. More credible

b. Less credible

22. What could be a source of bias in a study? Given an example of one that could be controlled pretty easily, and one that might be harder to control for.

23. Do you think that processing errors or non-adherence could affect some types of studies more than others? If so, how, what kinds? If not, why not?

24. What kind of things should we be careful about in conclusions of studies? (Think about clickbait headlines.)

25. Bring in a copy of a study from one of your previous courses or that you find online or in the library. Write a short paragraph critiquing the value of the study using what we learned in this chapter. What are some possible sources of bias in the study?

26. Give some specific examples of non-sampling errors.

27. What are the key features of a matched-pairs experiment?

28. How is a block design experiment different to or similar to a stratified sample?

29. An ad for Crest Whitestrips Premium claims that the strips will whiten teeth in 7 days and the results will last for 12 months. A researcher who wishes to test this claim studies 20 sets of identical twins. Within each set of twins, one is randomly assigned to use Crest Whitestrips Premium in addition to regular brushing and flossing, while the other twin is assigned to just regular brushing and flossing. Whiteness of teeth is measured at the beginning of the study, after 7 days and every month thereafter for 12 months.Fill in the graph of the experimental design below. Note how are subjects assigned to groups, what treatment are the two groups receiving (and number in each group if available), and finally, what and how often the response variable will be measured.

What kind of experimental model is this?

30. Read this article and be prepared to discuss it: http://io9.gizmodo.com/how-the-nocebo-effect-can-trick-us-into-actually-dyin-1681746203

31. Describe, or give an example, of the difference between a frequency distribution and a probability distribution.

32. What are the steps to create a pie chart?

33. What kind of data can go into a pie chart?

34. Comment on the quality of the following pie charts. Are they good, bad or misused?

a.

b.

c.

d.

35. What is the difference between a Pareto chart and a bar graph?

36. Below is a table of a cumulative distribution function for tossing 4 coins and counting the number of heads in each toss. Convert this cumulative distribution to a probability distribution.

# of Heads 0 1 2 3 4Probability (X ≤ x)

116

516

1116

1516

1

# of Heads 0 1 2 3 4Probability (X=x)

37. Complete the frequency distribution table below, and convert it to a relative frequency. What kind of graph would be appropriate for this data?

Class Students Percent (round to the nearest tenth)

Freshmen 8248

Sophomore 8073

Junior 7001

Senior 6904

Non-degree

Total 30761 100%

38. Construct a cumulative frequency table for the graph below.

Construct a cumulative frequency graph of the chart you created above.

39. The state affiliations of Presidents are shown in the table below by state (at the time of their elections, not their birth states). Use this information to create a Pareto chart of state affiliations.

# President State # President State

1 George Washington Virginia 23 Benjamin Harrison Indiana

2 John Adams Massachusetts 24 Grover Cleveland New York

3 Thomas Jefferson Virginia 25 William McKinley Ohio

4 James Madison Virginia 26 Theodore Roosevelt New York

5 James Monroe Virginia 27 William Howard Taft Ohio

6 John Quincy Adams Massachusetts 28 Woodrow Wilson New Jersey

7 Andrew Jackson Tennessee 29 Warren G. Harding Ohio

8 Martin Van Buren New York 30 Calvin Coolidge Massachusetts

9 William Henry Harrison Ohio 31 Herbert Hoover California

10 John Tyler Virginia 32 Franklin D. Roosevelt New York

11 James K. Polk Tennessee 33 Harry S. Truman Missouri

12 Zachary Taylor Louisiana 34 Dwight D. Eisenhower Kansas

13 Millard Fillmore New York 35 John F. Kennedy Massachusetts

14 Franklin Pierce New Hampshire 36 Lyndon B. Johnson Texas

15 James Buchanan Pennsylvania 37 Richard Nixon California

16 Abraham Lincoln Illinois 38 Gerald Ford Michigan

17 Andrew Johnson Tennessee 39 Jimmy Carter Georgia

18 Ulysses S. Grant Illinois [1] 40 Ronald Reagan California

19 Rutherford B. Hayes Ohio 41 George H. W. Bush Texas

20 James A. Garfield Ohio 42 Bill Clinton Arkansas

21 Chester A. Arthur New York [2] 43 George W. Bush Texas

22 Grover Cleveland New York 44 Barack Obama Illinois

40. Find an example of a display of qualitative data online to share with the class. It does not need to be one of the types discussed in the book, since there are many more we haven’t mentioned.

41. Describe how to calculate a class for quantitative data.

a. Use the data set on the age of presidents at inauguration and divide the data in 5 classes. Hint: You will find it helpful to sort the data first. (Use your calculator!)

President AGE (in years) President AGE (in years) George Washington 57 Benjamin Harrison 55John Adams 61 Grover Cleveland 55Thomas Jefferson 57 William McKinley 54James Madison 58 Theodore Roosevelt 42James Monroe 58 William Howard Taft 51John Quincy Adams 57 Woodrow Wilson 56Andrew Jackson 61 Warren G. Harding 55Martin Van Buren 54 Calvin Coolidge 51William Henry Harrison

68 Herbert Hoover 54

John Tyler 51 Franklin D. Roosevelt 51James K. Polk 49 Harry S. Truman 60Zachary Taylor 64 Dwight D. Eisenhower 62Millard Fillmore 50 John F. Kennedy 43Franklin Pierce 48 Lyndon B. Johnson 55James Buchanan 65 Richard Nixon 56Abraham Lincoln 52 Gerald Ford 61Andrew Johnson 56 Jimmy Carter 52Ulysses S. Grant 46 Ronald Reagan 69Rutherford B. Hayes 54 George H. W. Bush 64James A. Garfield 49 Bill Clinton 46Chester A. Arthur 51 George W. Bush 54Grover Cleveland 47 Barack Obama 47

b. Find the midpoint of each class.

42. How do histograms differ from bar charts?

43. For each of the graphs below comment on what type of graph it is (bar, Pareto, histogram), and whether it is good, bad, misused or misleading.

a.

b.

c.

d.

e.

f.

44. How can we use bar graphs to compare data? Why do we have to do the comparison differently for histograms and stemplots?

45. What are the steps in creating a stemplot? Take a problem from the textbook (2.1 #31-45), or use the president’s ages at inauguration above and use the stemplot grapher at http://www.calculatorsoup.com/calculators/statistics/stemleaf.php to create a stemplot for the data. In what way are stemplots better than histograms?

46. Below is a table of a cumulative distribution function for tossing 4 coins and counting the number of heads in each toss. Use this data to create an ogive graph.

# of Heads 0 1 2 3 4Probability (X ≤ x)

116

516

1116

1516

1

Below is the same situation as a probability distribution. Create a frequency polygon of the distribution.

# of Heads 0 1 2 3 4Probability (X=x)

116

14

38

14

116

47. In a cumulative frequency chart/graph, what is the highest value the chart/graph can have?

48. When creating a stem-and-leaf plot from 2-digit data, when should you split the 10s into groups of 5s instead?

49. The following is a stem-and-lead plot of 12 exam scores. (The stem is the tens place and the leaf is the ones place.) Redo the stem-and-leaf plot for the same data by splitting it into groups of 5s instead. Which one is better?

6 87 668 04889 22666

50. What kind of data is used when creating a line graph (typically)?

51. What kind of graphs are shown below. If there are problems with the graph, say what they are. Note: not all the graph types shown are covered in the book. If you encounter one, say so.

a.

b.

c.

d.

e.

f.

g.

h.

i.

52. Use Google or another search engine to find examples of each type of graph listed below to share with the class.a. Line graphb. Dot plotc. Stem-and-leaf plot (stemplot)d. Histograme. Bar chart or Pareto chartf. Frequency polygong. Ogive graphh. Pie chart

53. Describe the types of graphs used in this article: http://www.pewinternet.org/2015/12/11/public-interest-in-science-and-health-linked-to-gender-age-and-personality/