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Chapter 1: Q. 1.1 (page 14)
Use the data in the two-way table on page 12 to calculate the marginal distribution (in percents) of gender.
The Marginal Distribution for Female and for male marginal distribution is
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The chapter-opening Case Study described research by Teresa Amabile investigating whether external rewards would promote creativity in children鈥檚 artwork. Dr. Amabile conducted another study involving college students, who were divided into two groups using a chance process (like drawing names from a hat). The students in one group were given a list of statements about external reasons
(E) for writing, such as public recognition, making money, or pleasing their parents. Students in the other group were given a list of statements about internal reasons (I) for writing, such as expressing yourself and
enjoying playing with words. Both groups were then instructed to write a poem about laughter.
Each student鈥檚 poem was rated separately by different poets using a creativity scale. The poets鈥� ratings of each student鈥檚 poem were averaged to obtain an overall creativity score.
A dot-plot of the two groups鈥� creativity scores is shown below. Compare the two distributions. What do you conclude about whether external rewards promote creativity?
Baseball players (Introduction) Here is a small part of a data set that describes Major League Baseball players as of opening day of the 2009 season:
(a) What individuals does this data set describe?
(b) In addition to the player鈥檚 name, how many variables does the data set contain? Which of these variables are categorical and which are quantitative?
(c) What do you think are the units of measurement for each of the quantitative variables?
The Fathom dot plot displays data on the number of siblings reported by each student in a statistics class.
Describe the center of the distribution.
A study among the Pima Indians of Arizona investigated the relationship between a mother鈥檚 diabetic status and the appearance of birth defects in her children. The results appear in the two-way table below.
(a) Fill in the row and column totals in the margins of the table. (b) Compute (in percents) the conditional distributions of birth defects for each diabetic status. (c) Display the conditional distributions in a graph. Don鈥檛 forget to label your graph completely. (d) Comment on any clear associations you see.
Race and the death penalty Whether a convicted murderer gets the death penalty seems to be influenced by the race of the victim. Here are data on
cases in which the defendant was convicted of murder:
(a) Use these data to make a two-way table of the defendant鈥檚 race (white or black) versus the death penalty (yes or no).
(b) Show that Simpson鈥檚 paradox holds: a higher percent of white defendants are sentenced to death overall, but for both black and white victims a higher percent of black defendants are sentenced to death.
(c) Use the data to explain why the paradox holds in the language that a judge could understand.
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