EBK STATISTICS FOR BUSINESS & ECONOMICS
EBK STATISTICS FOR BUSINESS & ECONOMICS
12th Edition
ISBN: 8220100460463
Author: Anderson
Publisher: CENGAGE L
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Chapter 2.1, Problem 9E

The Pew Research Center’s Social & Demographic Trends project found that 46% of U.S. adults would rather live in a different type of community than the one where they are living now (Pew Research Center, January 29, 2009). The national survey of 2260 adults asked: “Where do you live now?” and “What do you consider to be the ideal community?” Response options were City (C), Suburb (S), Small Town (T), or Rural (R). A representative portion of this survey for a sample of 100 respondents is as follows.

Where do you live now?

S T R C R R T C S T C S C S T
S S C S S T T C C S T C S T C
T R S S T C S C T C T C T C R
C C R T C S S T S C C C R S C
S S C C S C R T T T C R T C R
C T R R C T C C R T T R S R T
T S S S S S C C R T          

What do you consider to be the ideal community?

S C R R R S T S S T T S C S T
C C R T R S T T S S C C T T S
S R C S C C S C R C T S R R R
C T S T T T R R S C C R R S S
S T C T T C R T T T C T T R R
C S R T C T C C T T T R C R T
T C S S C S T S S R          
  1. a. Provide a percent frequency distribution for each question.
  2. b. Construct a bar chart for each question.
  3. c. Where are most adults living now?
  4. d. Where do most adults consider the ideal community?
  5. e. What changes in living areas would you expect to see if people moved from where they currently live to their ideal community?

a.

Expert Solution
Check Mark
To determine

Construct the percent frequency distribution for each question.

Answer to Problem 9E

The percent frequency distribution for live now:

Live nowPercent frequency
City32%
Suburb26%
Small Town26%
Rural Area16%
Total100

The percent frequency distribution for Ideal Community:

Ideal CommunityPercent frequency
City24%
Suburb25%
Small Town30%
Rural Area21%
Total100

Explanation of Solution

The given information is that Pew Research Centers Social & Demographic Trends project show that 46% of U.S adults would rather live in a different type of community than where they are living now. In the national survey of 2,260 adults are asked two types of questions. A sample of 100 respondents is provided. The respective living areas are City, Suburb, Small Town and Rural Area.

Calculation:

For live now:

Frequency:

The frequencies are calculated by using the tally mark.

Here, the number of times each class repeats is the frequency of that particular class.

Here, “City” is repeated for 32 times in the data set and thus 32 is the frequency for the category City.

Similarly, the frequency of remaining types of living area is given below:

Live NowTallyFrequency
City||||||||||||||||||||||||||32
Suburb|||||||||||||||||||||26
Small Town|||||||||||||||||||||26
Rural Area|||||||||||||16
Total100

Relative frequency:

The general formula for the relative frequency is,

RelativeFrequency = FrequencyTotal frequency

Therefore,

RelativeFrequencyfor City=32100=0.32

Similarly, the relative frequencies for the remaining types of living area are obtained below:

Live NowFrequencyRelative frequency
City320.32
Suburb260.26
Small Town260.26
Rural Area160.16
Total1001.00

Percentage frequency distribution:

The general formula for the percent frequency is,

Percent Frequency=RelativeFrequency×100

Therefore,

Percent Frequencyfor City=0.32×100=32%

The percent frequencies for the remaining types of categories of living area for live now are obtained below:

Live NowRelative frequencyPercent frequency
City0.3232%
Suburb0.2626%
Small Town0.2626%
Rural Area0.1616%
Total1.00100

For ideal community:

Here, city is repeated for 24 times in the data set and thus 24 is the frequency for the living area city.

Similarly, the frequency of remaining types of living area is given below:

Ideal communityTallyFrequency
City||||||||||||||||||||24
Suburb||||||||||||||||||||25
Small Town||||||||||||||||||||||||30
Rural Area|||||||||||||||||21
Total100

Relative frequency:

RelativeFrequencyfor city=24100=0.24

Similarly, the relative frequencies for the remaining types of living area are obtained below:

Ideal communityFrequencyRelative frequency
City240.24
Suburb250.25
Small Town300.30
Rural Area210.21
Total1001.00

Percentage frequency distribution:

Percent Frequencyfor city=0.24×100=24%

The percent frequencies for the remaining types of categories of living area of ideal community are obtained below:

Ideal communityRelative FrequencyPercent frequency
City0.2424%
Suburb0.2525%
Small Town0.3030%
Rural Area0.2121%
Total1.00100

b.

Expert Solution
Check Mark
To determine

Construct the bar chart for each question.

Explanation of Solution

Output obtained from MINITAB software for live now is:

EBK STATISTICS FOR BUSINESS & ECONOMICS, Chapter 2.1, Problem 9E , additional homework tip  1

Output obtained from MINITAB software for Ideal community is:

EBK STATISTICS FOR BUSINESS & ECONOMICS, Chapter 2.1, Problem 9E , additional homework tip  2

Calculation:

For live now:

Software procedure:

Step by step procedure to draw the bar chart for bachelor’s degree using MINITAB software.

  • Choose Graph > Bar Chart.
  • From Bars represent, choose unique values from table.
  • Choose Simple. Click OK.
  • In Graph variables, enter the column of Live now.
  • Click OK
  • For ideal community:

Step by step procedure to draw the bar chart for Master’s degree using MINITAB software.

  • Choose Graph > Bar Chart.
  • From Bars represent, choose unique values from table.
  • Choose Simple. Click OK.
  • In Graph variables, enter the column of Ideal Community.
  • Click OK

c.

Expert Solution
Check Mark
To determine

Find the living area where the most adults are living now.

Answer to Problem 9E

The most adults in living now consider a City.

Explanation of Solution

For living now, the percentage for city is 32%, which is high when compared to other categories.

d.

Expert Solution
Check Mark
To determine

Find the living area which the most adults are considered as an ideal community.

Answer to Problem 9E

The most adults consider the ideal community is a small town.

Explanation of Solution

For ideal, the percentage for small town is 30%, which is high when compared to other categories.

e.

Expert Solution
Check Mark
To determine

Identify the changes in living areas would expect to see if people moved from where they currently live to their ideal community.

Explanation of Solution

The percentage changes can be obtained as follows:

Difference=Idealcommunity  percent frequencyliving nowpercent frequency

Therefore,

Difference for City=(Ideal Community percent frequency for CityLiving Now percent frequencyfor City)=24%32%=8%

The differences between two living areas are tabulated below:

Living AreaLiving nowIdeal communityDifference
City32%24%–8%
Suburb26%25%–1%
Small Town26%30%4%
Rural Area16%21%5%

From the table, it is observed that the living areas “small town and rural area” has increased in percentage from “living now” to “ideal community” and the living areas “city and suburb” has decrease in percentage from “living now” to “ideal community”.

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Chapter 2 Solutions

EBK STATISTICS FOR BUSINESS & ECONOMICS

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