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Practice Problems



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1. Identify the level of measurement for each of the following variables:

(A) Type of residence (i.e., dorm, off-campus apartment, condominium, or parent’s home, other)


(B) Height in inches


(C) The rating of the overall quality of a textbook on a scale from “Excellent” to “Poor”


(D) Lab section


(E) Level of measurement


2. For each of the following research questions, identify the unit of analysis, the independent variable, and the dependent variable:

(A) Are social movement participation rates higher in countries that have a longer history of democratic rule?


(B) Do school districts with more highly educated teachers tend to have higher standardized test scores among the students in the district?


3. Assume that the answers to the research questions in Problem 2 are both yes. Consider the following additional variables that go with the above questions:

(A) median household income of the country


(B) median household income of the school district


For each research question, decide whether the additional variable is most likely to be a source of spuriousness, a possible mechanism, or a possible modifier of the implied relationships in question 2. Explain each answer in one or two sentences and draw a diagram showing how each additional variable is related to the independent and dependent variables from each part of Question 2.


[Note that mechanism and mediator and intervenor are synonymous and that interactionspecification, and modification are synonyms.]


4. Among many other things, the United Nations Development Program collects data from various countries on the percentage of the adult workforce made up by women. Here are the percentages for 25 countries included in a study done by the program in the mid-1990’s: 37; 39; 46; 39; 46; 42; 39; 27; 48; 39; 42; 42; 45; 45; 42; 39; 30; 47; 42; 30; 37; 42; 46; 42; 42.


Show your work for each of the following (for repetitive calculations, such as relative frequency, you only have to show work for the first few repetitions):


(A) Determine absolute and relative frequencies (i.e., proportions) of each value as well as the cumulative relative frequencies at each point. Do this by filling out a table that follows the following format:


% women in the workforce ( X) Frequency


Relative Frequency ( p) Relative Cumulative Frequencyp)
27 1 4 4
30 2 8 12
37 2 8 20
39 5 20 40
42 8 32 72
45 2 8 80
46 3 12 92
47 1 4 96
48 1 4 100



(Note: you should include as many rows as you need to display frequencies for each data value). Do not group the data into class intervals. Instead, use one row for each value present in the dataset.


(B) Plot your data on a frequency histogram. Now you will need to group your data into class intervals. Describe how you determine the intervals.


(C) Describe the shape of your frequency histogram.








Example 1-1: Department vs. College
Male Female
# of applicants % admitted # of applicants % admitted
College 2175 47 0 849 31
Dept A 825 62 108 82 511.5 88.56
Dept B 560 63 25 68 352.8 17
Dept C 417 33 375 35 137.61 131.25
Dept D 373 6 341 7 22.38 23.87
1024.29 260.68






Tabular Graphic Numerical
Univariate Discrete Nominal Frequency Table Bar Chart Mode
Ordinal Mode, Median, Mean
Continuous Interval Histogram
Bivariate Discrete-Discrete Contingency Table TBC TBC


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