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Chapter 2: Q36. (page 94)
Calculate the mean for samples where
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Question: In business, do nice guys really finish last?Do 鈥渘ice guys finish last鈥� in the competitive corporate world? In a study published in Nature(March 20, 2008), college students repeatedly played a version of the game 鈥減risoner鈥檚 dilemma,鈥� where competitors choose cooperation, defection, or costly punishment. (Cooperation meant paying 1 unit for the opponent to receive 2 units; defection meant gaining 1 unit at a cost of 1 unit for the opponent, and punishment meant paying 1 unit for the opponent to lose 4 units.) At the conclusion of the games, the researchers recorded the average payoff and the number of times punishment was used against each player. A graph of the data
is shown in the accompanying scatterplot. Does it appear that average payoff is associated with punishment use? The researchers concluded that 鈥渨inners don鈥檛 punish.鈥� Do you agree? Explain.
Using only integers between 0 and 10, construct two data sets with at least 10 observations each so that the two sets have the same mean but different variances. Construct dot plots for each of your data sets and mark the mean of each data set on its dot diagram.
Do social robots walk or roll? A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 6414, 2010), design engineers investigated the trend in the design of social robots. Using a random sample of 106 social robots obtained through a Web search, the engineers found that 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. This information is portrayed in the accompanying graph.
a. What type of graph is used to describe the data?
b. Identify the variable measured for each of the 106 robot designs.
c. Use the graph to identify the social robot design that is currently used the most.
d. Compute class relative frequencies for the different categories shown in the graph.
e. Use the results from part d to construct a Pareto diagram for the data.
U.S. business bankruptcies.The American Bankruptcy Institute and the National Bankruptcy Research Center monitor the number of business bankruptcy filings each quarter. The table below lists the number of business bankruptcy filings for each quarter of a recent 2-year period. FILING
a.Explain why the data in the table represent time series data.
b.Construct a time series plot for the quarterly number of bankruptcy filings.
c.Do you detect a trend in the time series plot? Explain.
Year | Quarter | Number of Bankruptcies |
2011 | 1 2 3 4 | 12,376 12,304 11,705 11,149 |
2012 | 1 2 3 4 | 10,998 10,374 9,248 9,231 |
Consider the following two sample data sets.
Sample A | Sample B |
121, 171, 158, 173, 184, 163, 157, 85, 145, 165, 172, 196, 170, 159, 172, 161, 187, 100, 142, 166, 171 | 171, 152, 170, 168, 169, 171, 190, 183, 185, 140, 173, 206, 172, 174, 169, 199, 151, 180, 167, 170, 188 |
a.Construct a box plot for each data set.
b.Identify any outliers that may exist in the two data sets.
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