1. Identify the level of measurement for each of the following variables:
(A) Region of birth
(B) Favorite academic subject (rank 1, 2, 3, etc.)
(C) Weight in pounds
(D) Opinion of President Bush (Favorable, Neutral, Unfavorable)
(E) Verbal SAT Score
(F) Year in College
(G) College Major
2. For each of the following research questions, identify the unit of analysis, the independent variable, and the dependent variable:
(A) Do poorer neighborhoods have higher rates of former prisoners living in them?
(B) Are children of fathers who have not attended college less likely to attend college?
(C) Are individuals who are high school dropouts less likely to vote than those with more education?
3. Assume that the answers to the research questions in Problem 2 are all yes. Consider the following additional variables that go with the above questions:
(B) family income
For each research question, decide whether the additional variable is a possible 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. (You should end up with 3 explanations and 3 diagrams).
[Note that mechanism and mediator are synonyms and that interaction, specification, and modification are synonyms.]
4. Suppose that a professor is interested in determining how much time her students spend on studying. On a Monday morning, she decided to conduct a survey of her class in which she asked students to list the number of hours they spent on their coursework during the past two days. The numbers reported by each student were as follows:
7, 5, 12, 10, 8, 6, 33, 13, 8, 7, 11, 10, 6, 9, 43, 7, 9, 8, 11, 9, 10, 38, 12, 9, 11.
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:
|Hours doing coursework ( X)||Frequency ( f)||Relative Frequency ( p)||Relative Cumulative Frequency ( p)|
(Note: you should include as many rows as you need to display frequencies for each data value). Do not use “grouped frequencies” (as discussed on p.37-38) in the rows of this table – in other words, do not group the data into class intervals. Instead, use every possible value in the entire range as a row.
(B) Plot your data on a frequency histogram. This time you will need to group your data into class intervals. Follow the example provided in Figure 2.2, p.42. Explain how you picked your intervals.
(C) Describe the shape of your frequency histogram.