Elementary Statistics

Robert Johnson, Patricia Kuby

Chapter 1

Statistics - all with Video Answers

Educators

Section 1

What is Statistics?

Problem 1

Postyour.info is a worldwide service where Internet users from arround the world can take part in questionnaires [http)/postyour.info/] Below is a graph depicting the combined summary of how users answered one of the posted questions. Results given in Percent (count).
a. What question was asked and answered in order to gather the information presented on this graph?
b. Who was asked the question?
c. How many people answered the question?
d. Verify the percentages $1.59 \%, 17.46 \%,$ and $25.4 \%$
e. Are the percentages reported in this graph likely to be representative of all people? Explain why or why not.

Rashmi Sinha

Rashmi Sinha

Numerade Educator

Problem 2

Do you work hard for your money? Java professionals think they do, reporting long working hours at their jobs. Java developers from around the world were surveyed about the number of hours they work weekly. Listed here are the average number of hours worked weekly in various regions of the United States and the world.
$$\begin{array}{lclc}
\text { Region } & \text { Hours Worked } & \text { Region } & \text { Hours Worked } \\
\hline \text { U.S. } & 48 & \text { Colíornia } & 50 \\
\text { Northeast } & 47 & \text { Pocific NW } & 47 \\
\text { Mid-Allantic } & 49 & \text { Carado } & 43 \\
\text { South } & 47 & \text { Europe } & 48 \\
\text { Midwest } & 47 & \text { Asio } & 47 \\
\text { Centrol } M & 51 & \text { South America } & 49 \\
& & \text { and Africa } & \\
\hline
\end{array}$$
a. How many hours do you work per week (or anticipate working after you graduate)?
b. What happened to the 40 -hour workweek? Does it appear to exist for the Java professional?
c. Does the information in this chart make a career as a Java professional seem attractive?

Hailey Tomashek

Hailey Tomashek

Numerade Educator

Problem 3

1.3 a. Each of the statistical graphics presented on the first page of this chapter seems to suggest that information is about what population? Is that the case? Justify your answer.
b. Describe the information that was collected and used to determine the statistics reported in "Are you fretting about messages?"
c. $\quad$ "47\%- One hour or less" was one specific statistic reported in "Are you fretting about messages?" Describe what that statistic tells you.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 4

a. Consider the graphic "How often is your bed made?" If you had been asked, how would you have responded? What does the percentage associated with your answer mean? Explain.
b. How do you interpret the "5\% - Weekly" reported in "How often is your bed made?"

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 5

a. Write a 50 -word paragraph describing what the word "statistics" means to you right now.
b. Write a 50 -word paragraph describing what the word "random" means to you right now.
- c. Write a 50 -word paragraph describing what the word "sample" means to you right now.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 6

Statistics is defined on page 1 as "the science of collecting, describing, and interpreting data." Using your own words, write a sentence describing each of the three statistical activities. Retain your work for Exercise 1.79

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 7

Determine which of the following statements is descriptive in nature and which is inferential. Refer to "How old is my fish?" in Applied Example 1.1 (p. 1).
a. All 9 -inch large mouth bass in New York State are an average of three years old.
b. Of the large mouth bass used in the sample to make up the $N Y S$ DEC Freshwater Fishing Guide, the average age of 9 -inch large mouth bass was three years.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 8

Determine which of the following statements is descriptive in nature and which is inferential. Refer to "Many teens use phones in class" in Applied Example $1.2(\mathrm{p} .2)$
a. $84 \%$ of the surveyed teens in May and June of 2009 had cell phones.
b. In May/June $2009,16 \%$ of all teens did not have a cell phone.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 9

Refer to the graphic "Setting a Date for Date Night."
a. What group of people were polled?
b. How many people were polled?
c. What information was obtained from each person?
d. Explain the meaning of "18\% say once every $4-6$ months"
e. How many people answered "Once every $4-6$ months"?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 10

International Communications Research (ICR) conducted the 2008 Spring Cleaning Survey for the Soap and Detergent Association. ICR questioned 777 American adults who spring-clean about which spring cleaning chore they would like to hire someone to do for them. The "chore" results were: $47 \%$ washing windows, $23 \%$ cleaning the bathroom, $12 \%$ cleaning the kitchen, $8 \%$ dusting, $7 \%$ mopping, $3 \%$ other. The survey has a margin of error of plus or minus $3.52 \%$
a. What is the population?
b. How many people were polled?
c. What information was obtained from each person?
d. Using the information given, estimate the number of surveyed adults who would gladly hire someone
to wash the windows, if they could.
e. What do you think the "margin of error of plus or minus $3.52 \%$ "means?
f. How would you use the "margin of error" in estimating the percentage of all adults who would like to hire out the spring-cleaning chore of "Cleaning the kitchen"?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 11

Opinion Research Corporation conducted the 2009 Lemelson-MIT Invention Index survey of 501 teens, ages 12-17. The teens were asked what everyday invention they thought would be obsolete in five years. Refer to the graphic "In One Day, Out the Next."
a. What is the population?
b. How many people were polled?
c. What information was obtained from each person?
d. Estimate the number of surveyed teens who thought the computer mouse will be obsolete in five years.
e. What do you think the "margin of error" of ±4.3 percentage points means?
f. How would you use the "margin of error" in estimating the percentage of all teens who thought the computer mouse will be obsolete in five years?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 12

Refer to the graphic on next page "What do you Plan to Spend your Tax Refund on?" (page 12 ).
a. Describe the population of interest.
b. Describe the sample most likely used for this report.
c. Identify the variables used to collect this information.
d. What were the majority of people going to do with their tax refund? How does this majority show on the graph?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 13

During a radio broadcast a few years ago, David Essel reported the following three statistics: (1) the U.S. divorce rate is $55 \%,$ and when married adults were asked if they would remarry their spouse, (2) $75 \%$ of the women said yes, and (3) $65 \%$ of the men said yes.
a. What is the "stay married" rate?
b. There seems to be a contradiction in this information. How is it possible for all three of these statements to be correct? Explain.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 14

A working knowledge of statistics is very helpful when you want to understand the statistics reported in the news. The news media and our government often make a statement such as, "Crime rate jumped $50 \%$ in your city."
a. Does an increase in rate from 4 to 6 represent an increase of $50 \% ?$ Explain.
b. Why would anybody report an increase from 4 to 6 as
$a^{-1} 50 \%$ rate jump"?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 15

Of the adult U.S. population, $36 \%$ has an allergy. A sample of 1200 randomly selected adults resulted in
$33.2 \%$ having an allergy.
a. Describe the population.
b. What is the sample?
c. Describe the variable.
d. Identify the statistic and give its value.
e. Identify the parameter and give its value.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 16

Find a recent newspaper article that illustrates an "apples are bad" type of report.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 17

In your own words, explain why the parameter is fixed and the statistic varies.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 18

Is a football jersey number a quantitative or a categorical variable? Support your answer with a detailed explanation.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 19

a. Name two customer-related attribute variables that a newly opened department store might find informative to study.
b. Name two customer-related numerical variables that a newly opened department store might find informative to study.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 20

a. Name two customer-related nominal variables that a newly opened department store might find informative to study.
b. Name two customer-related ordinal variables that a newly opened department store might find informative to study.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 21

Simulates taking a sample of size 10 from a population of 100 college students. Take one sample and note the outcome.
a. Name the attribute variable involved in this experiment. Is it nominal or ordinal?
b. Name the numerical variable involved in this experiment. Is it discrete or continuous?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 22

a. Explain why the variable "score" for the home team at a basketball game is discrete.
b. Explain why the variable "number of minutes to commute to work" is continuous.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 23

The severity of side effects experienced by patients who are being treated with a particular medicine is under study. The severity is measured on a scale of none, mild, moderate, severe, very severe.
a. Name the variable of interest.
b. Identify the type of variable.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 24

A nationwide poll of adults on cell phone use and driving was conducted during May 2009 by the Harris Poll.Their responses to "How dangerous is it for a driver to use a cell phone while driving?" were categorized as "very dangerous," "dangerous," "somewhat dangerous," "slightly dangerous," or "not dangerous at all."
a. Name the variable of interest.
b. Identify the type of variable.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 25

Students are being surveyed about the weight of books and supplies they are carrying as they attend class.
a. Identify the variable of interest.
b. Identify the type of variable.
c. List a few values that might occur in a sample.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 26

A drug manufacturer is interested in the proportion of persons with hypertension (elevated blood pressure) whose condition can be controlled by a new drug the company has developed. A study involving 5000 individuals with hypertension is conducted, and it is found that $80 \%$ of the individuals are able to control their hypertension with the drug. Assuming that the 5000 individuals are representative of the group that has hypertension, answer the following questions:
a. What is the population?
b. What is the sample?
c. Identify the parameter of interest.
d. Identify the statistic and give its value.
e. Do we know the value of the parameter?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 27

The admissions office wants to estimate the cost of textbooks for students at our college. Let the variable $x$ be the total cost of all textbooks purchased by a student this semester. The plan is to randomly identify 100 students and obtain their total textbook costs. The average cost for the 100 students will be used to estimate the average cost for all students.
a. Describe the parameter the admissions office wishes to estimate.
b. Describe the population.
c. Describe the variable involved.
d. Describe the sample.
e. Describe the statistic and how you would use the data collected to calculate the statistic.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 28

A quality-control technician selects assembled parts from an assembly line and records the following information concerning each part:
X: defective or nondefective
Y: the employee number of the individual who assembled the part $\mathrm{Z}:$ the weight of the part
a. What is the population?
b. Is the population finite or infinite?
c. What is the sample?
d. Classify the three variables as either attribute or numerical.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 29

Select 10 students currently enrolled at your college and collect data for these three variables:
$\mathrm{X}:$ number of courses enrolled in
Y: total cost of textbooks and supplies for courses
$\mathrm{Z}:$ method of payment used for textbooks and supplies
a. What is the population?
b. Is the population finite or infinite?
c. What is the sample?
d. Classify the three variables as nominal, ordinal, discrete, or continuous.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 30

A study was conducted by Aventis Pharmaceuticals Inc. to measure the adverse side effects of Allegra"M, a drug used for the treatment of seasonal allergies. A sample of 679 allergy sufferers in the United States was given
$60 \mathrm{mg}$ amounts of the drug twice a day. The patients were to report whether or not they experienced relief from their allergies as well as any adverse side effects (viral infection, nausea, drowsiness, etc.).
Source: Good Housekeeping, February 2005
a. What was the population being studied?
b. What was the sample?
c. What were the characteristics of interest about each element in the population?
d. Were the data being collected qualitative or quantitative?

Sheryl Ezze

Numerade Educator

Problem 31

On the next page is a small sample of the 1652009 pickup trucks listed on MPGoMatic.com and available to the buying public. Refer to the table for this exercise (1.31) on page 14.
a. What was the population from which this sample was taken?
b. How many individuals were in the population? In the sample?
c. How many variables?
d. Name the qualitative/categorical variables.
e. Which of the qualitative variables are nominal? Ordinal?
f. $\quad$ Name the quantitative variables.
g. Which of the quantitative variables are discrete? Continuous?

James Kiss

Numerade Educator

Problem 32

Applet Exercise simulates taking a sample of size 10 from a population of 100 college students. Take a sample of size $10 .$
a. What is the population?
b. Is the population finite or infinite?
c. $\quad$ Name two parameters and give their values.
d. What is the sample?
e. $\quad$ Name the two corresponding statistics and give their values.
f. Take another sample of size $10 .$ Which of the items above remain fixed and which changed?

Jon Southam

Numerade Educator

Problem 33

Identify each of the following as examples of (1) attribute (qualitative) or ( 2 ) numerical (quantitative) variables:
a. The breaking strength of a given type of string
b. The hair color of children auditioning for the musical Annie
c. The number of stop signs in towns of fewer than 500 people
d. Whether or not a faucet is defective
e. The number of questions answered correctly on a standardized test
f. The length of time required to answer a telephone call at a certain real estate office

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 34

Identify each of the following as examples of (1) nominal, (2) ordinal, (3) discrete, or (4) continuous variables:
a. $\quad$ A poll of registered voters as to which candidate they support
b. The length of time required for a wound to heal when a new medicine is being used
c. The number of televisions within a household
d. The distance first-year college women can kick a football
e. The number of pages per job coming from a computer printer
f. The kind of tree used as a Christmas tree

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 35

Suppose a 12 -year-old asked you to explain the difference between a sample and a population.
a. What information should your answer include?
b. What reasons would you give him or her for why one would take a sample instead of surveying every member of the population?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 36

Suppose a 12 -year-old asked you to explain the difference between a statistic and a parameter.
a. What information should your answer include?
b. What reasons would you give him or her for why one would report the value of a statistic instead of the value of a parameter?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator