Chapter 1.1, Problem 30E

a.

To determine

To find the distribution of superpower preferencefor the students in the sample from each country (the United States and the United Kingdom).To make a segmented bar graph to compare these distributions.

Answer to Problem 30E

The result for the distribution of superpower preferencefor the students in the sample from each country (the United States and the United Kingdom)is as below:

Superpower	Country
	U.K.	U.S.
Fly	27%	20.93%
Freeze time	26%	20.47%
Invisibility	15%	17.21%
Superstrength	10%	10.70%
Telepathy	22%	30.70%

The segmented bar graph to compare these distributions is as below:

  

Explanation of Solution

Given:

The study includes 415 children from the United Kingdom and the United States who completed a survey in a recent year. Each students countryof origin was recorded along with which superpower they would most like to have: theability to fly, ability to freeze time, invisibility, superstrength, or telepathy (ability to readminds). The data are summarized in the following table.

Superpower	Country
	U.K.	U.S.
Fly	54	45
Freeze time	52	44
Invisibility	30	37
Superstrength	20	23
Telepathy	44	66

Concept Used:

Let us first determine the column total of each column, which is the sum of all counts in the corresponding column. Then determine the distribution of superpower preference from each country, by dividing the counts by the column total. Finally, make a segmented bar graph to compare these distributions.

Calculation:

Determine the column total of each column from the given table.

Superpower	Country
	U.K.	U.S.
Fly	54	45
Freeze time	52	44
Invisibility	30	37
Superstrength	20	23
Telepathy	44	66
Column Total	$54+52+30+20+44=200$	$45+44+37+23+66=215$

Determine the distribution of superpower preference from each country,by dividing the counts by the column total as shown in the below table:

Superpower	Country
	U.K.	U.S.
Fly	$\frac{54}{200}=\frac{27}{100}=0.27=27\%$	$\frac{45}{215}=\frac{9}{43}\approx 0.2093=20.93\%$
Freeze time	$\frac{52}{200}=\frac{13}{50}=0.26=26\%$	$\frac{44}{215}\approx 0.2047=20.47\%$
Invisibility	$\frac{30}{200}=\frac{3}{20}=0.15=15\%$	$\frac{37}{215}\approx 0.1721=17.21\%$
Superstrength	$\frac{20}{200}=\frac{1}{10}=0.10=10\%$	$\frac{23}{215}\approx 0.1070=10.70\%$
Telepathy	$\frac{44}{200}=\frac{11}{50}=0.22=22\%$	$\frac{66}{215}\approx 0.3070=30.70\%$

Create a segmented bar graph, where in the width of each bars should be equal and the height should be equal to the percentage of superpowers as shown below.

  

b.

To determine

To describe the association between country of origin and superpower preferencefor the students in the sample from the segmented bar graph obtained in part (a).

Answer to Problem 30E

We note that the most popular superpower in the U.S. appears to be telepathy, while the most popular superpowers in the U.K. appear to be freeze time and fly.

We also note that the superstrength appears to be the least popular superpower in both the countries.

Explanation of Solution

We note that the most popular superpower in the U.S. appears to be telepathy, while the most popular superpowers in the U.K. appear to be freeze time and fly as shown from the bar graph obtained in part (a).

We also note that the superstrength appears to be the least popular superpower in both the countriesas shown from the bar graph obtained in part (a).