1. An art professor was interested in seeing what size group is best to prime the pump so to speak to encourage strangers to gather together in front of various exhibits at her art show, so she set up an experiment. In a municipal building off campus, she asked a group of two students to stand next to each other and stare intently at a wall decoration while simultaneously she asked a group of five students to do the same at the other end of the floor. For the next 30 minutes she observed passersby to see if they too looked at the decorations for more than five seconds or made comments about the artwork to members of the either group.
Here is what she found: She observed 9 people make comments or look at the decorations for more than five seconds with respect to group of two (G2). Down the hallway, she observed 26 people look at the decorations or make comments to the group of five (G5). However, she found that 34 people just passed by G5 without noticing the decoration or making a comment. A smaller number (31) just walked past G2. Because G5 had more passers than participants, she concluded that placing two of her students in front of art displays would encourage strangers to do the same. Was this a good decision? Please support your answer with an appropriate test.
2. A professor is interested in knowing the correlation, if any, of students' scores on the first and second exams given in his class.
|
Test 1
|
Test 2
|
|
92
|
86
|
|
90
|
87
|
|
89
|
85
|
|
82
|
90
|
|
88
|
79
|
|
92
|
90
|
|
100
|
92
|
|
91
|
84
|
Is there a significant correlation? Explain its statistical significance, if any.
3. With respect to the situation in question 16, what other test could the professor use that would yield valid results by looking for differences. What would be the statistical result of the test?
4. Now, let's look at a situation in which we compare three college math teachers to each other with respect to how interested they keep their students. The study was conducted among freshmen enrolled in an introductory course. The unit was quadratic equations. Students were asked to jot down an x on a piece of paper every time they found their attention drifting away from the lecture.
Here are data from one fifty minute lecture:
Teacher A Teacher B Teacher C
5 9 4
5 7 4
7 4 6
4 7 5
6 8 6
6 7 5
5 4 4
5 5 6
43 51 40
What test or tests would you use to rule out chance from causing the apparent differences in these data?
5. What are the results of running the test on the data in question 18?
6. A professor teaches two different subjects (history and sociology) in an ethnically diverse college. She wants to know how much interest students have in prominent political figures. She reasons that knowing this will help her plan for future lectures.
She asked students to rate each person listed with a Lickert scale (a continuum with five being high and 1 being of low interest). Upon looking at the data results, she concluded that there is no need to emphasize any political figure more than the others. Indeed, she reckoned, students in each subject area rated the figures similarly, so she can pace her lessons just as she has in the past.
History students' scores:
John Maynard Keynes 3.6
Jesus 4.1
Martin Luther King Jr. 4.0
Karl Marx 2.5
Patricia Ireland 2.6
Abraham Lincoln 4.5
Sociology students' scores:
John Maynard Keynes 3.7
Jesus 4.2
Martin Luther King Jr. 3.9
Karl Marx 4.1
Patricia Ireland 4.0
Abraham Lincoln 3.8
Is her conclusion solid? Please provide a statistical assessment using Spearman rs to evaluate her decision. Explain the practical significance of the test as well as its implications, if any, for her decision.