Q 43. The chapter-opening Case Study d... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 1: Q 43. (page 43)

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 $12$ different poets using a creativity scale. The $12$ 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?

Short Answer

Expert verified

The term "spread" refers to the median, and the mode of distribution E would have higher spread than distribution I. In distribution E, there is a distinct peak, however, this peak is not evident in distribution I.

Step by step solution

Given information

The graph is:

Concept

Dot plots are one of the most fundamental statistical plots, and they work best with small to medium-sized data sets.

Calculation

The ranges of the dot-plots for external reasons (E) and internal reasons (I) are nearly comparable. However, as compared to distribution E, distribution I is more asymmetrical.

In E, the distribution ranges from $5$ to $24$ is $24 - 5 = 19$

And the distribution range in E is from $5$ to $24$ is $30 - 12.5 = 17.5$

As a result, distribution E's spread means, median, and mode would have a higher spread than distribution I's. Outliers exist in distribution E, whereas they do not exist in distribution I. In distribution E, there is a distinct peak, however, this peak is not evident in distribution I.