Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

133E

Expert-verified
Statistics For Business And Economics
Found in: Page 132
Statistics For Business And Economics

Statistics For Business And Economics

Book edition 13th
Author(s) James T. McClave, P. George Benson, Terry Sincich
Pages 888 pages
ISBN 9780134506593

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later
Illustration

Short Answer

Best-paid CEOs. Refer to Glassdoor Economic Research firm’s 2015 ranking of the 40 best-paid CEOs in Table 2.1 (p. 65). Recall that data were collected on a CEO’s current salary, age, and the ratio of salary to a typical worker’s pay at the firm.

a. Create a scatterplot to relate a CEO’s ratio of salary to worker pay to the CEO’s age. Comment on the strength of the association between these two variables.

b. Conduct an outlier analysis of the ratio variable. Identify the highly suspect outlier in the data.

c. Remove the highly suspect outlier from the data and recreate the scatterplot of part a. What do you observe?

a. The graph is given below:

No strong association

b.Highly suspect outlier = 1951

c. No major change

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Creating a Scatterplot

The graph is given below:

There is no visible strong association between the CEO’s age and the ratio of the CEO’s salary to that of a typical worker. The data is clustered to the left of the graph except for a few scattered points.

Conducting an outlier analysis and identifying the highly suspect outliers

We will use the box plot method to conduct an outlier analysis on the ratio variable.

We will first calculate the quartiles, IQR, Inner, and Outer fences.

Arranging the data in ascending order,

Q1=N+14=40+14=414=10.25th

Term = 483

Q2=N+12=40+12=412= 20.25th

Term = 536.5

Q3=3N+14=340+14=1234= 30.75th

Term = 644.25

IQR = QU– QL = 644.25 – 483 = 161.25

Lower Inner Fence = QL−1.5IQR = 483–1.5161.25 = 483–241.875 = 241.125

Upper Inner Fence = QU+ 1.5IQR = 644.25 + 1.5161.25 = 644.25 + 241.875 = 886.125

Now we will plot these,

The graph shows that the outliers are 1951, 1522, 1192, 1133, and 939.

To find which of these are highly suspect outliers (with a z-score > 3), we will check the z-score of these outliers.

First, we will calculate the mean and standard deviation of the data.

Mean =Sum of all observationsNo. of observations= 2567040= 641.75

Variance = ∑χ−2n−1=386417039= 99081.28

Standard Deviation =Variance=99081.28=314.77

Mean = 641.75 and Standard Deviation = 314.77

z-score of 1951=1951−641.75314.77=1309.25314.77=4.159

z-score of 1522 =1522−641.75314.77=880.25314.77= 2.79

Based on the values of the z-score, 1522 is not a highly suspect outlier. Therefore, none of the values lower than 1522 are outliers.

So, the only highly suspect outlier is 1951.

Creating a scatterplot without the highly suspect outlier.

1951 is a highly suspect outlier. Therefore, we will remove that from the data and create the scatterplot.

There is not much difference in the scatterplot after removing the highly suspect outlier.

Most popular questions for Math Textbooks

Question: Construct a scatterplot for the data in the following table.

Variable 1: 5 1 1.5 2 2.5 3 3.5 4 4.5 5

Variable 2: 2 1 3 4 6 10 9 12 17 17

Consider the following three measurements: 0, 4, and 12. Find the z-score for each measurement if they are from a population with the following mean and standard deviation equal to

a. µ = 2 and σ = 1

b. µ = 4 and σ = 2

c. µ = 8 and σ = 2

d. µ = 8 and σ = 8

Most valuable NFL teams. Refer to the Forbes listing of the 2015 values of the 32 teams in the National Football League (NFL), Exercise 2.26 (p. 84). Construct a scatterplot to investigate the relationship between 2015 value ($ millions) and operating income ($ millions). Would you recommend that an NFL executive use operating income to predict a team’s current value? Explain.

Do social robots walk or roll? A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 6414, 2010), design engineers investigated the trend in the design of social robots. Using a random sample of 106 social robots obtained through a Web search, the engineers found that 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. This information is portrayed in the accompanying graph.

a. What type of graph is used to describe the data?

b. Identify the variable measured for each of the 106 robot designs.

c. Use the graph to identify the social robot design that is currently used the most.

d. Compute class relative frequencies for the different categories shown in the graph.

e. Use the results from part d to construct a Pareto diagram for the data.

Top credit card issuers, by region. The Nilson Report (December 2015) published a list of the top 150 credit card issuers worldwide. The issuers (e.g., American Express, MasterCard, Visa) were ranked based on outstanding debt during the year. The table gives a breakdown of the regions in the world served by the top 150 credit card issuers.

Worldwide Region

Number of credit card issuers

Asia-Pacific

48

Canada

10

Europe

34

Latin America

29

Middle East/Africa

3

United States

26

Total

150

a. One of the top 150 credit card issuers is selected at random, and the region it serves is determined. What type of data (quantitative or qualitative) is measured?

b. For each region in the table, calculate the percentage of the 150 top credit card issuers that fall into that region.

c. Use the percentages, part b, to construct a relative frequency bar graph for the data summarized in the table.

d. Based on the bar graph, make a statement about the regions that most of the top 150 credit card users serve.
Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Math Textbooks

Decision Maths

Read explanation

Probability and Statistics

Read explanation

Statistics

Read explanation

Mechanics Maths

Read explanation

Geometry

Read explanation

Calculus

Read explanation

Pure Maths

Read explanation

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.