Practice Quiz 2: on Chapters 4 and 8 and crowd counting

Instructions: Answer each question, and when required explain your answer. Your explanation must be clear and complete. You may refer to your book, your notes and your homework papers.

John and Jane get stuck watching the baby. They are told to watch the baby for a total of 10 hours (6 hours in the morning and 4 in the afternoon). They agree to use the two player divide and choose method to split babysitting hours between them. In order to keep his morning hours down, John is willing to do 2 afternoon hours for each morning hour. For Jane, the hours are all the same. Assume John is the divider. If he were to create two schedules, both with 3 morning hours and 2 afternoon hours, he realizes he'd be stuck doing 3 morning hours in addition to 2 afternoon hours no matter what. Knowing that Jane doesn't care so much when she does her hours, how might John divide the hours into two schedules that he would see as having equal value but which would minimize his morning shift? Explain what you think John would do (and why), and how you think Jane would choose.
Judy, Sam and Terri agree to divide a carton of Neapolitan ice cream (which has 12 ounces each of chocolate, vanilla and strawberry). They agree to use the three person lone chooser method, in which Judy divides the carton into two portions of equal value to her. Then Sam picks one of these two and gives the other to Judy. Finally, Sam and Judy each divide their portions into three pieces of what they see as having equal value, at which point Terri picks one portion each from Judy and Sam.
Assume Judy hates chocolate but likes vanilla and strawberry the same. She decides therefore to make one portion with 6 oz chocolate and 12 oz vanilla, with the other portion being 6 oz chocolate and 12 oz strawberry. Thus no matter what Sam picks, Judy can get stuck with at most half of the chocolate. Assume Sam hates chocolate and vanilla but loves strawberry. Thus Sam leaves Judy the vanilla-chocolate portion and keeps the strawberry-chocolate portion. Judy now cuts her portion into three pieces. She cuts the vanilla into three equal pieces and puts the chocolate with one of those pieces. Thus the three pieces are: a 4 oz portion of vanilla, another 4 oz portion of vanilla, and a third portion which is 4 oz vanilla plus 6 oz chocolate. Sam divides his portion into: a 4 oz portion of strawberry, another 4 oz portion of strawberry, and a third portion which is 4 oz strawberry plus 6 oz chocolate.
- (a) Assume Terri loves strawberry, likes vanilla a little but hates chocolate. What choices might Terri make?
- (b) Is the end result envy free, or does someone prefer what someone else got? Indicate each person who prefers what someone else got. Explain your answer.
(Be prepared to make other kinds of charts too.)
- Make a double stem and leaf plot using the two data sets given in Problem 4 on page 512.
- Make a single comparison histogram using the two data sets given in Problem 4 on page 512. Choose an appropriate bin length; justify the length you use.
(Be prepared to discuss the advantages of other kinds of charts.) A survey of college students found that 67% have an after school job, 45% live off campus, 43% ride a bicycle to class, and 25% have not declared a major. Which would be the best choice to display this data: a bar chart, a line graph, a pie chart or a histogram? Justify your answer as to which is best (and why each of the others are not).
Do Problem 4 on page 545.
What would be a good way to measure the size of a crowd at concert? What would be a good way to measure the size of a crowd at a political demonstration? Discuss whether each method you mention would or would not be good (and why) for the other situation.