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Chapter 1: Q 50. (page 48)
Pair-a-dice The dotplot shows the results of rolling a pair of fair, six-sided dice and Page Number: 48 finding the sum of the up-faces 100 times. Describe the shape of the distribution.
Roughly symmetric
Single peak
No gaps
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Birth months Imagine asking a random sample of 60 students from your school about their birth months. Draw a plausible (believable) graph of the distribution of birth months. Should you use a bar graph or a histogram to display the data?
Marginal totals aren鈥檛 the whole storyHere are the row and column totals for a two-way table with two rows and two columns:
Find two different sets of counts a, b, c, and dfor the body of the table that give these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.
Simpson鈥檚 paradoxAccident victims are sometimes taken by helicopter from the accident scene to a hospital. Helicopters save time. Do they also save lives? The two-way table summarizes data from a sample of patients who were transported to the hospital by helicopter or by ambulance.
(a) What percent of patients died with each method of transport? Here are the same data broken down by severity of accident:
(b) Calculate the percent of patients who died with each method of transport for the serious accidents. Then calculate the percent of patients who died with each method of transport for the less serious accidents. What do you notice?
(c) See if you can explain how the result in part (a) is possible given the result in part (b).
Note: This is an example of Simpson鈥檚 paradox, which states that an association between two variables that holds for each value of a third variable can be changed or even reversed when the data for all values of the third variable are combined.
Where do the young live? Here is a stemplot of the percent of residents aged 25 to 34 in each of the 50 states:
Part (a). Why did we split stems?
Part (b). Give an appropriate ate key for this stemplot.
Part (c). Describe the shape of the distribution. Are there any outliers?
The Dallas Mavericks won the NBA championship in the 2010鈥�2011 season. The two-way table displays the relationship between the outcome of each game in the regular season and whether the Mavericks scored at least 100 points.
Which of the following is the best evidence that there is an association between the outcome of a game and whether or not the Mavericks scored at least 100 points?
(a) The Mavericks won 57 games and lost only 25 games.
(b) The Mavericks scored at least 100 points in 47 games and fewer than 100 points in only 35 games.
(c) The Mavericks won 43 games when scoring at least 100 points and only 14 games when scoring fewer than 100 points.
(d) The Mavericks won a higher proportion of games when scoring at least 100 points (43/47) than when they scored fewer than 100 points (14/35).
(e) The combination of scoring 100 or more points and winning the game occurred more often (43 times) than any other combination of outcomes.
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