Statistics Informed Decisions Using Data

Michael Sullivan III

Chapter 1

Data Collection - all with Video Answers

Educators

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Section 1

Introduction to the Practice of Statistics

Problem 1

Define statistics

Donna Densmore

Donna Densmore

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Problem 2

Explain the difference between a population and a sample.

Harsh Gadhiya

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Problem 3

A(n) _____ is a person or object that is a member of the population being studied.

Harsh Gadhiya

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Problem 4

______ statistics consists of organizing and summarizing information collected, while _____ statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.

Harsh Gadhiya

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Problem 5

A(n) _____ s a numerical summary of a sample. A(n) _____ is a numerical summary of a population.

Emily Himsel

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Problem 6

_____ are the characteristics of the individuals of the population being studied.

Harsh Gadhiya

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Problem 7

Determine whether the underlined value is a parameter or a statistic.
Following the 2014 national midterm election, $18 \%$ of the governors of the 50 United States were female. Source: National Governors Association

Donna Densmore

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Problem 8

Determine whether the underlined value is a parameter or a statistic.
The average score for a class of 28 students taking a calculus midterm exam was $72 \%$.

Harsh Gadhiya

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Problem 9

Determine whether the underlined value is a parameter or a statistic.
In a national survey of 1300 high school students (grades 9 to 12 ), $32 \%$ of respondents reported that someone had bullied them at school. Source: Bureau of Justice Statistics

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Problem 10

In a national survey on substance abuse, $9.6 \%$ of respondents aged 12 to 17 reported using illicit drugs within the past month.

James Kiss

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Problem 11

Ty Cobb is one of Major League Baseball's greatest hitters of all time, with a career batting average of $0.366 .$

James Kiss

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Problem 12

Only 12 men have walked on the moon. The average time these men spent on the moon was 43.92 hours.

James Kiss

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Problem 13

A study of 6076 adults in public rest rooms (in Atlanta, Chicago, New York City, and San Francisco) found that $23 \%$ did not wash their hands before exiting.

James Kiss

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Problem 14

Interviews of 100 adults 18 years of age or older, conducted nationwide, found that $44 \%$ could state the minimum age required for the office of U.S. president.

James Kiss

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Problem 15

Classify the variable as qualitative or quantitative.
Nation of origin

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Problem 16

Classify the variable as qualitative or quantitative.
Number of siblings

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Problem 17

Classify the variable as qualitative or quantitative.
Grams of carbohydrates in a doughnut

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Problem 18

Classify the variable as qualitative or quantitative.
Number on a football player's jersey

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Problem 19

Classify the variable as qualitative or quantitative.
Number of unpopped kernels in a bag of microwave popcorn

Emily Himsel

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Problem 20

Classify the variable as qualitative or quantitative.
Assessed value of a house

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Problem 21

Classify the variable as qualitative or quantitative.
Phone number

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Problem 22

Classify the variable as qualitative or quantitative.
Student ID number

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Problem 23

Determine whether the quantitative variable is discrete or continuous.
Goals scored in a season by a soccer plaver

Emily Himsel

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Problem 24

Determine whether the quantitative variable is discrete or continuous.
Volume of water lost each day through a leaky faucet

Harsh Gadhiya

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Problem 25

Determine whether the quantitative variable is discrete or continuous.
Length (in minutes) of a country song

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Problem 26

Determine whether the quantitative variable is discrete or continuous.
Number of Sequoia trees in a randomly selected acre of Yosemite National Park

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Problem 27

Determine whether the quantitative variable is discrete or continuous.
High temperature on a randomly selected day in Memphis, Tennessee

Emily Himsel

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Problem 28

Determine whether the quantitative variable is discrete or continuous.
Internet connection speed in kilobytes per second

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Problem 29

Determine whether the quantitative variable is discrete or continuous.
Points scored in an NCAA basketball game

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Problem 30

Determine whether the quantitative variable is discrete or continuous.
Air pressure in pounds per square inch in an automobile tire

Harsh Gadhiya

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Problem 31

Determine the level of measurement of each variable.
Nation of origin

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Problem 32

Determine the level of measurement of each variable.
Movie ratings of one star through five stars

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Problem 33

Determine the level of measurement of each variable.
Volume of water used by a household in a day

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Problem 34

Determine the level of measurement of each variable.
Year of birth of college students

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Problem 35

Determine the level of measurement of each variable.
Highest degree conferred (high school, bachelor’s, and so on)

Emily Himsel

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Problem 36

Determine the level of measurement of each variable.
Eye color

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Problem 37

Determine the level of measurement of each variable.
Assessed value of a house

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Problem 38

Determine the level of measurement of each variable.
Time of day measured in military time

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Problem 39

A research objective is presented. For each, identify the population and sample in the study.
The Gallup Organization contacts 1028 teenagers who are 13 to 17 years of age and live in the United States and asks whether or not they had been prescribed medications for any mental disorders, such as depression or anxiety.

Harsh Gadhiya

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Problem 40

A research objective is presented. For each, identify the population and sample in the study.
A quality-control manager randomly selects 50 bottles of Coca-Cola that were filled on October 15 to assess the calibration of the filling machine.

Harsh Gadhiya

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Problem 41

A research objective is presented. For each, identify the population and sample in the study.
A farmer interested in the weight of his soybean crop randomly samples 100 plants and weighs the soybeans on each plant.

Emily Himsel

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Problem 42

A research objective is presented. For each, identify the population and sample in the study.
Every year the U.S. Census Bureau releases the Current Population Report based on a survey of 50,000 households. The goal of this report is to learn the demographic characteristics. such as income, of all households within the United States.

Harsh Gadhiya

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Problem 43

A research objective is presented. For each, identify the population and sample in the study.
Folate and Hypertension Researchers want to determine whether or not higher folate intake is associated with a lower risk of hypertension (high blood pressure) in women ( 27 to 44 years of age). To make this determination, they look at 7373 cases of hypertension in these women and find that those who consume at least 1000 micrograms per day $(\mu \mathrm{g} / \mathrm{d})$ of total folate had a decreased risk of hypertension compared with those who consume less than $200 \mu \mathrm{g} / \mathrm{d}$.

Joseph Thublin

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Problem 44

A research objective is presented. For each, identify the population and sample in the study.
A community college notices that an increasing number of full-time students are working while attending the school. The administration randomly selects 128 students and asks how many hours per week each works.

James Kiss

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Problem 45

Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete.
The following data represent driver's license laws for yarious states.

James Kiss

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Problem 46

Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete.
The following information relates to the 2011 model year product line of BMW automobiles.$$\begin{array}{llcc}\text { Model } & \text { Body Style } & \text { Weight (lb) } & \text { Number of Seats } \\\hline \text { 3 Series } & \text { Coupe } & 3362 & 4 \\\hline \text { 5 Series } & \text { Sedan } & 4056 & 5 \\\hline \text { 6 Series } & \text { Convertible } & 4277 & 4 \\\hline \text { 7 Series } & \text { Sedan } & 4564 & 5 \\\hline \text { X3 } & \text { Sport utility } & 4012 & 5 \\\hline \text { Z4 } & \text { Roadster } & 3505 & 2 \\& \text { Coune } &\end{array}$$

James Kiss

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Problem 47

A study was conducted in which 20,211 18-year-old Israeli male military recruits were given an exam to measure IQ. In addition, the recruits were asked to disclose their smoking status. An individual was considered a smoker if he smoked at least one cigarette per day. The goal of the study was to determine whether adolescents aged 18 to 21 who smoke have a lower IQ than nonsmokers. It was found that the average IQ of the smokers was $94,$ while the average IQ of the nonsmokers was 101 . The researchers concluded that lower IQ individuals are more likely to choose to smoke, not that smoking makes people less intelligent.
(a) What is the research objective?
(b) What is the population being studied? What is the sample?
(c) What are the descriptive statistics?
(d) What are the conclusions of the study?

Joseph Thublin

Numerade Educator

Problem 48

A study conducted by researchers was designed "to determine if application of duct tape is as effective as cryotherapy (liquid nitrogen applied to the wart for 10 seconds every 2 to 3 weeks) in the treatment of common warts."The researchers randomly divided 51 patients into two groups. The 26 patients in group 1 had their warts treated by applying duct tape to the wart for 6.5 days and then removing the tape for 12 hours, at which point the cycle was repeated for a maximum of 2 months. The 25 patients in group 2 had their warts treated by cryotherapy for a maximum of six treatments. Once the treatments were complete, it was determined that $85 \%$ of the patients in group 1 and $60 \%$ of the patients in group 2 had complete resolution of their warts. The researchers concluded that duct tape is significantly more effective in treating warts than cryotherapy.
(a) What is the research objective?
(b) What is the population being studied? What is the sample?
(c) What are the descriptive statistics?
(d) What are the conclusions of the study?

Joseph Thublin

Numerade Educator

Problem 49

Gallup News Service conducted a survey of 1017 American adults aged 18 years or older, September $4-7,2014 .$ The respondents were asked, "Of every tax dollar that goes to the federal government in Washington, D.C. how many cents of each dollar would you say are wasted?" Of the 1017 individuals surveyed, $35 \%$ indicated that 51 cents or more is wasted. Gallup reported that $35 \%$ of all adult Americans 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of $4 \%$ and a $95 \%$ level of confidence.
(a) What is the research objective?
(b) What is the population?
(c) What is the sample?
(d) List the descriptive statistics.
(e) What can be inferred from this survey?

Joseph Thublin

Numerade Educator

Problem 50

The Gallup Organization conducted a survey of 1018 adults, aged 18 and older, living in the United States and asked, "If you had a thousand dollars to spend, do you think investing it in the stock market would be a good or bad idea?" Of the 1018 adults, $46 \%$ said it would be a bad idea. The Gallup Organization reported that $46 \%$ of all adults, aged 18 and older, living in the United States thought it was a bad idea to invest $\$ 1000$ in the stock market with a $4 \%$ margin of error with $95 \%$ confidence.
(a) What is the research objective?
(b) What is the population?
(c) What is the sample?
(d) List the descriptive statistics.
(e) What can be inferred from this survey?

Joseph Thublin

Numerade Educator

Problem 51

It is extremely important for a researcher to clearly define the variables in a study because this helps to determine the type of analysis that can be performed on the data. For example, if a researcher wanted to describe baseball players based on jersey number, what level of measurement would the variable jersey number be? Now suppose the researcher felt that certain players who were of lower caliber received higher numbers. Does the level of measurement of the variable change? If so, how?

Jennifer Stoner

Jennifer Stoner

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Problem 52

Suppose a fundraiser holds a raffle for which each person who enters the room receives a ticket numbered 1 to $N,$ where $N$ is the number of people at the fundraiser. The first person to arrive receives ticket number 1 , the second person receives ticket number $2,$ and so on. Determine the level of measurement for each of the following interpretations of the variable ticket number.
(a) The winning ticket number.
(b) The winning ticket number was announced as $329 .$ An attendee noted his ticket number was 294 and stated, "I guess I arrived too early."
(c) The winning ticket number was announced as $329 .$ An attendee looked around the room and commented, "It doesn't look like there are 329 people in attendance."

Rashmi Sinha

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Problem 53

Read the newspaper article and answer the following questions:
(a) What is the research question the study addresses?
(b) What is the sample?
(c) What type of variable is season in which you were born?
(d) What can be said (in general) about individuals born in summer? Winter?
(e) What conclusion was drawn from the study?

Rashmi Sinha

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Problem 54

Contrast the differences between qualitative and quantitative variables.

Harsh Gadhiya

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Problem 55

Discuss the differences between discrete and continuous
variables

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Problem 56

In your own words, define the four levels of measurement of a variable. Give an example of each.

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Problem 57

Explain what is meant when we say "data vary." How does this variability affect the results of statistical analysis?

Harsh Gadhiya

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Problem 58

Explain the process of statistics.

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Problem 59

The age of a person is commonly considered to be a continuous random variable. Could it be considered a discrete random variable instead? Explain.

Harsh Gadhiya

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