3.11: Collaborative Activity
- Page ID
- 59222
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In this collaborative activity your group will run a designed experiment that will investigate how the method used for rolling a die possibly affects the outcomes of the die rolls. The purpose of this activity is to participate in an experiment and experience first-hand the possible problems associated with experimentation and data observation.
For this collaborative activity you will need the following materials:
- A regular six-sided die.
- A flat surface on which the die can land during the experiment.
- A hardcover book that can be used as a short ramp.
- A cup suitable for shaking the die.
Before starting the activity, you will need to assign members of your group to the following roles:
- A data manager who will oversee collecting the data from the experiment.
- A person in charge of rolling the die.
The roles can be shared when there are additional members in the group.
The experiment:
- The first part of the experiment will consider rolling the die using the method most often employed by game players: holding the die in the palm of one’s hand and rolling it on a table. Be sure the table is clear, so the die does not encounter any obstructions. If the die rolls off of the table, do not use that observation and roll again. Using this method the die roller should roll the die 50–100 times (depending on how much time is allotted for the activity). The data manager should keep track of each of the rolls using the data sheet shown below.
Roll Palm Book Cup Roll Palm Book Cup 1 51 2 52 3 53 4 54 5 55 6 56 7 57 8 58 9 59 10 60 11 61 12 62 13 63 14 64 15 65 16 66 17 67 18 68 19 69 20 70 21 71 22 72 23 73 24 74 25 75 26 76 27 77 28 78 29 79 30 80 31 81 32 82 33 83 34 84 35 85 36 86 37 87 38 88 39 89 40 90 41 91 42 92 43 93 44 94 45 95 46 96 47 97 48 98 49 99 50 100 - The next part of the experiment will consider what happens when the die is rolled in a very deliberate way. In this case a hard cover book should be placed on a table. The book should be larger than a usual paperback novel. With the book closed, the die should be place on the top cover near the edge opposite of the spine with the face with a single dot as the top face. Next, slowly open the book cover until the die slides down the cover and rolls on the table. Using this method the die roller should roll the die 40–80 times (depending on how much time is allotted for the activity). The data manager should keep track of each of the rolls using the data table.
- The final part of the experiment uses the cup to roll the die. For each roll, the die should be placed into the cup and shaken before rolling the die out onto the table. Once again, the die roller should roll the die 40–80 times with the data manager keeping track of the rolls on the data table.
-
The table shown below provides an example of how the data table should look at the end of the experiment. For the example, we used 25 rolls of the die using each method. For the first method, the first roll was 5, following by a roll of 1, and then a roll of 4. The data was recorded in the first three rows of the column labeled “Palm”. The remaining numbers in the column correspond to the remaining observations from the example experiment using the “Palm” method of rolling the die. Similarly, the first three observed rolls for the “Book” method were 6, 5, and 3, and the first three observed rolls for the “Cup” method were 6, 3, and 5, with the remaining observations for each method continuing down the corresponding columns.
Roll
Palm
Book
Cup
1
5
6
6
2
1
5
3
3
4
3
5
4
3
1
1
5
4
4
5
6
6
2
3
7
5
5
3
8
4
2
4
9
6
5
3
10
4
2
4
11
6
4
6
12
3
1
2
13
4
4
6
14
3
2
3
15
3
2
4
16
3
4
1
17
6
4
1
18
1
5
2
19
2
4
4
20
1
4
6
21
2
5
6
22
3
2
6
23
2
4
6
24
4
2
3
25
3
6
2
Calculations:
-
Once the observations have been collected, construct a table like the one shown in below. The calculations contained in this table will allow us to investigate how the three different methods of rolling the die affect the observed outcomes of the rolls.
Outcomes
Method
1
2
3
4
5
6
Palm
Book
Cup
- For the first calculation, count how many times each of the die faces is observed for the first method of rolling the die, and report these counts in the row labeled “Palm".
- Next, count how many times each of the die faces is observed for the second method of rolling the die, and report these counts in the row labeled “Book”.
- Finally, count how many times each of the die faces is observed for the third method of rolling the die, and report these counts in the row labeled “Cup”.
-
The table shown below contains the results of these calculations that have been done for the example data shown earlier. In the first column of the row labeled “Palm,” we have entered a 3 for the example data. If you look down the “Palm” column of the table below, you will see that we observed a roll of 1 three times. Similarly, there were three times when a roll of 2 was observed in that column, and seven times that a roll of 3 was observed in that column. The remaining entries of the table are computed in a similar manner.
Outcomes
Method
1
2
3
4
5
6
Palm
3
3
7
6
2
4
Book
2
7
1
8
5
2
Cup
3
3
6
4
2
7
Questions:
- Suppose the method of rolling the die has absolutely no effect on the behavior of the die in terms of how often each of the faces is observed. What do you think the results observed in the table showing the number of oucomes in each category would look like? Would they always be the same? How do the results that you observed in your experiment compare to what would be expected?
- Regardless of the data that was observed during your experiment, do you believe that the rolling method influences the behavior of the die? What is the reason for these beliefs? How do your personal feelings about the methods compare to what you observed? Are you surprised by the results?
- Were there any practical problems that you encountered while doing the experiment? What were they? What types of changes could be made in the experiment to make it run easier?
- Can you think of anything about the experiment that might produce bias in the results? Are there any possible confounding factors that could be problematic when interpreting the results of the experiment? How might these problems be addressed?