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Fundamentals of Statistics

Michael Sullivan III

Chapter 1

Data Collection - all with Video Answers

Educators


Section 1

Introduction to the Practice of Statistic

00:44

Problem 1

Define statistics.

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01:00

Problem 2

Explain the difference between a population and a sample.

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00:15

Problem 3

Statistics is the science of collecting, organizing, summarizing, and analyzing ________________ to answer questions or draw conclusions.

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00:34

Problem 4

$\mathrm{A}(\mathrm{n})$ ____________ is a person or object that is a member of the population being studied.

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01:10

Problem 5

_________________ 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.

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00:19

Problem 6

What does it mean when an experiment is double-blind?

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00:37

Problem 7

Discuss the differences between an experimental group and a control group.

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00:25

Problem 8

What are placebos? Why do you think they are needed?

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00:30

Problem 9

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

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03:55

Problem 10

Contrast the differences between qualitative and quantitative variables.

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01:06

Problem 11

Discuss the difference between discrete and continuous variables.

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00:12

Problem 12

True or False: Both discrete and continuous variables are quantitative variables.

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01:12

Problem 13

Explain the process of statistics.

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00:53

Problem 14

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

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00:35

Problem 15

Classify the variable as qualitative or quantitative.
Nation of origin

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00:54

Problem 16

Classify the variable as qualitative or quantitative.
Number of siblings

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00:27

Problem 17

Classify the variable as qualitative or quantitative.
Eye color

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00:32

Problem 18

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

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00:24

Problem 19

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

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00:18

Problem 20

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

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00:20

Problem 21

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

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00:26

Problem 22

Assessed value of a house
Phone number

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00:11

Problem 23

Classify the variable as qualitative or quantitative.
Population of a state

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00:18

Problem 24

Classify the variable as qualitative or quantitative.
cost (in dollars) to fill up a 2005 Chevrolet Corvette

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00:20

Problem 25

Classify the variable as qualitative or quantitative.
Student ID number

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00:12

Problem 26

Classify the variable as qualitative or quantitative.
Marital status

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00:13

Problem 27

Determine whether the quantitative variable is discrete or continuous.
Runs scored in a season by Albert Pujols

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00:22

Problem 28

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

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00:48

Problem 29

Determine whether the quantitative variable is discrete or continuous.
Length of a country song

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00:33

Problem 30

Determine whether the quantitative variable is discrete or continuous.
At rest pulse rate of a 20 -year-old college student

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00:18

Problem 31

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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00:31

Problem 32

Determine whether the quantitative variable is discrete or continuous.
Weight of a randomly selected hog

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00:25

Problem 33

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

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00:25

Problem 34

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

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00:16

Problem 35

Determine whether the quantitative variable is discrete or continuous.
Number of tornadoes in a year in the United States

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00:15

Problem 36

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

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00:13

Problem 37

Determine whether the quantitative variable is discrete or continuous.
Number of donors at a blood drive

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00:21

Problem 38

Determine whether the quantitative variable is discrete or continuous.
Number of donors at a blood drive

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00:28

Problem 39

A research objective is presented. For each research objective, identify the population and sample in the study.
The Gallup Organization contacts 1,028 teenagers who are 13 to 17 years of age and live in the United States and asked whether or not they had been prescribed medications for any mental disorders, such as depression or anxiety.

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00:49

Problem 40

A research objective is presented. For each research objective, 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.

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00:24

Problem 41

A research objective is presented. For each research objective, identify the population and sample in the study.
A farmer wanted to learn about the weight of his soybean crop. He randomly sampled 100 plants and weighed the soybeans on each plant.

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00:50

Problem 42

A research objective is presented. For each research objective, 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 of all households within the United States, such as income.

Harsh Gadhiya
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00:26

Problem 43

A research objective is presented. For each research objective, identify the population and sample in the study.
Folate and Hypertension Researcher John P. Forman and co-workers wanted to determine whether or not higher folate intake is associated with a lower risk of hypertension (high blood pressure) in younger women (27 to 44 years of age). To make this determination, they looked at 7,373 cases of hypertension in younger women and found that younger women who consumed at least 1,000 micrograms per day $(\mu \mathrm{g} / \mathrm{d})$ of total folate (dietary plus supplemental) had a decreased risk of hypertension compared with those who consumed less than $200 \mu \mathrm{g} / \mathrm{d} .$ (Source: "Folate intake and the risk of incident hypertension among US Women," John P. Forman, MD; Eric B. Rimm, ScD; Meir J. Stampfer, MD; Gary C. Curhan, MD, ScD; Journal of the American Medical Association $293(2005): 320-329)$

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00:17

Problem 44

A research objective is presented. For each research objective, identify the population and sample in the study.
A large community college has noticed that an increasing number of full-time students are working while attending the school. The administration randomly selects 128 students and asks this question: How many hours per week do you work?

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00:50

Problem 45

For the studies in Problems $45-50,$ (a) identify the research objective, (b) identify the sample, (c) list the descriptive statistics, and (d) state the conclusions made in the study.
A Cure for the Common Wart A study conducted by reIsearchers was designed "to determine if application of duct tape is as effective as cryotherapy 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 (liquid nitrogen applied to the wart for 10 seconds every 2 to 3 weeks) for a maximum of 6 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. (Source: "The Efficacy of Duct Tape vs. Cryotherapy in the Treatment of Verruca Vulgaris (The Common Wart)," Dean R. Focht III, Carole Spicer, Mary P. Fairchok; Archives of Pediatrics and Adolescent Medicine, Vol. 156
No. $10,$ October 2002 )

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00:39

Problem 46

For the studies in Problems $45-50,$ (a) identify the research objective, (b) identify the sample, (c) list the descriptive statistics, and (d) state the conclusions made in the study.
Early Epidurals A study was conducted at Northwestern University in Chicago to determine if pregnant women in first-time labor could receive low-dose epidurals, an anesthesis to control pain during childbirth early without raising their chances of a Caesarean section. In the study, reported in the New England Journal of Medicine, "728 women in first-time labor were divided into two groups. One group received the spinal shot and then got epidurals when the cervix dilated to about 2 centimeters. The other group initially received pain-relieving medicine directly into their bloodstreams, and put off epidurals until 4 centimeters if they could tolerate the pain." In the end, the Csection rate was $18 \%$ in the early epidural group and $21 \%$ in the delayed group. The researchers concluded that pregnant women in first-time labor can be given a low-dose epidural early without raising their chances of a C-section. (Source: Associated Press, Feb. 22, 2005)

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00:43

Problem 47

For the studies in Problems $45-50,$ (a) identify the research objective, (b) identify the sample, (c) list the descriptive statistics, and (d) state the conclusions made in the study.
The Mozart Effect Researchers at the University of California, Irvine, wished to determine whether "music cognition and cognitions pertaining to abstract operations such as mathematical or spatial reasoning" were related. To test the research question, 36 college students listened to Mozart's Sonata for Two Pianos in D Major, K488, for 10 minutes and then took a spatial reasoning test using the Stanford-Binet intelligence scale. The same students also took the test after sitting in a room for 10 minutes in complete silence. Whether the student experienced Mozart first or silence first was randomly determined. The average score on the test following the Mozart piece was $119,$ while the average test score following the silence was 110. The researchers concluded that subjects performed better on abstract and spatial reasoning tests after listening to Mozart. (Source: "Music and Spatial Performance," Frances H. Rauscher et al.; Nature 365,14 October 1993: 611 )

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00:43

Problem 48

For the studies in Problems $45-50,$ (a) identify the research objective, (b) identify the sample, (c) list the descriptive statistics, and (d) state the conclusions made in the study.
Favorite Presidents A poll commissioned by Washington College and conducted by Schulman, Ronca, and Bucuvalas, February $7-10,2005,$ surveyed 800 U.S. adults. Asked who was the greatest president, $20 \%$ of respondents chose Abraham Lincoln, $15 \%$ Ronald Reagan, $12 \%$ Franklin Roosevelt, $11 \%$ John $\mathrm{F}$. Kennedy, $10 \%$ Bill Clinton, $8 \%$ George W. Bush, and $6 \%$ George Washington. The remaining $18 \%$ selected other presidents. Washington College concluded that Abraham Lincoln ranks first among U.S. adults as the greatest president. (Source: Associated Press, Feb. 22, 2005)

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00:47

Problem 49

For the studies in Problems $45-50,$ (a) identify the research objective, (b) identify the sample, (c) list the descriptive statistics, and (d) state the conclusions made in the study.
Go to the Movies? Gallup News Service conducted a survey of 1,003 American adults aged 18 years or older, December $5-8,2004 .$ The respondents were asked, "How many movies, if any, have you attended in a movie theater in the past 12 months?" Of the 1,003 adults surveyed, $65 \%$ said they attended at least one movie in a movie theater in the past 12 months. Gallup News Service concluded that $65 \%$ of all Americans aged 18 years or older attended at least one movie in a movie theater in the past 12 months.

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00:41

Problem 50

For the studies in Problems $45-50,$ (a) identify the research objective, (b) identify the sample, (c) list the descriptive statistics, and (d) state the conclusions made in the study.
Morally Acceptable? Gallup News Service conducted a survey of 1,000 U.S. adults aged 18 years or older, May $2-4,2004 .$ The respondents were asked, "Do you believe that having a baby outside of marriage is morally acceptable or morally wrong?" Of the 1,000 adults surveyed, $49 \%$ said that having a baby outside of marriage is moralIy acceptable. Gallup News Service concluded that $49 \%$ of all U.S. adults 18 years or older believe that having a baby outside of marriage is morally acceptable.

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02:02

Problem 51

Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. (FIGURE CAN'T COPY)
Widescreen TVs The following data relate to widescreen high-definition televisions.

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01:28

Problem 52

Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. (FIGURE CAN'T COPY)
BMW Cars The following information relates to the entire product line of BMW automobiles.

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02:03

Problem 53

Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. (FIGURE CAN'T COPY)
Driver's License Laws The following data represent driver's license laws for various states.

Trent Speier
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02:00

Problem 54

Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. (FIGURE CAN'T COPY)
MP3 Players The following information concerns various MP3 players that can be purchased online at circuitcity.com:

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00:39

Problem 55

Read the newspaper article and identify (a) the research question the study addresses, (b) the population, (c) the sample, $(d)$ the descriptive statistics, and (e) the inferences of the study.
By Jeff Donn Associated Press February 20,2005
BOSTON-Levels of a stress-related protein in the blood could give doctors a powerful new tool for deciding which patients with clogged heart arteries are most in danger and need aggressive treatment, a study found.

This protein is yet another predictor of heart trouble, in addition to such substances as cholesterol and C-reactive protein.

The Danish study, published in Thursday's New England Journal of Medicine, focused on a substance called B-natriuretic peptide, or BNP, released into the blood when the heart is stressed. Some doctors already test for this protein to help evaluate patients with shortness of breath who may be suffering from congestive heart disease.

The researchers measured the protein levels in 1,034 patients and followed their health for nine years. People with the highest protein levels were $2 \frac{1}{2}$ times more likely to die from any cause than those with the lowest.

This protein could help doctors decide which patients need angioplasty or heart-bypass surgery. "It sort of tells you that no matter what condition you have, higher levels of these peptides are associated with worse outcomes," said cardiologist Dr. James de Lemos, at the University of Texas Southwestern Medical Center.

Kimberly Waterbury
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01:32

Problem 56

Read the newspaper article and identify (a) the research question the study addresses, (b) the population, (c) the sample, $(d)$ the descriptive statistics, and (e) the inferences of the study.
Study: Exercise May Prevent Parkinson's By Kathleen Fackelmann, USA Today Men who engaged in regular, vigorous exercise as teens and young adults drastically cut their risk of developing Parkinson's disease later in life, a study reports Tuesday. As many as 1 million people in the USA, including actor Michael J. Fox, have this progressive neurological disease, which commonly strikes after age $50 .$
In addition to suggesting that exercise could ward off the disease, the findings also raise the hope that physical activity might help hold the line on brain cell destruction in people who already have it.Robin Elliott, executive director of the Parkinson's Disease Foundation in New York, said the study is promising because there is no cure for Parkinson's. Doctors today have no way to stop or delay the progression of the disease, which affects the brain region that controls movement. Common symptoms of Parkinson's are tremors and a shuffling gait. Researcher Alberto Ascherio of the Harvard School of Public Health and his colleagues studied 48,000 men and 77,000 women who were relatively healthy and middle-aged or older at the study's start. Over the course of the study, 387 people developed the disease. The team did a statistical analysis to look for a link between physical activity and the risk of Parkinson's. Men who said they jogged, played basketball or participated in some other vigorous activity at least twice a week in high school, college and up to age 40 had a $60 \%$ reduced risk of getting Parkinson's, says the study, which was published today in Neurology. The team found no such protection for women. But the women in this study came of age in the '50s and '60s, an era when young women did not have as many opportunities to participate in sports. Ascherio says. The study had so few female athletes that any protection may have been missed, he says. This study's findings are supported by animal research: Michael Zigmond, a researcher at the University of Pittsburgh and his colleagues have reported that exercise protects rats from developing a Parkinson's-like disease. No one knows for certain whether exercise can prevent or delay the symptoms of Parkinson's in humans. But there is plenty of evidence suggesting that a regular fitness regimen might ward off a host of ailments as diverse as heart disease and Alzheimer's. That leads experts such as Zigmond to recommend a vigorous workout on most days of the week. "We know that exercise is good for you in ways that go beyond any one condition."

Kimberly Waterbury
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01:10

Problem 57

Read the newspaper article and identify (a) the research question the study addresses, (b) the population, (c) the sample, $(d)$ the descriptive statistics, and (e) the inferences of the study.
Nominal versus Ordinal Just as a quantitative variable can be further classified as discrete or continuous, we can classify a qualitative (or categorical) variable as nominal or ordinal. A nominal variable is a qualitative variable that describes an attribute of an individual. An ordinal variable is a qualitative variable that has all the properties of a nominal variable, but also has observations that can be ranked or put in order. For example, gender is a nominal variable, whereas a response to a customer satisfaction survey of poor, fair, good, or outstanding is considered ordinal. For each of the following qualitative variables, determine whether the variable is nominal or ordinal.
(a) Hair color
(b) Letter grade in a statistics class
(c) Make of a television set
(d) Rank of a military officer
(e) Method of payment (cash, check, debit card, credit card)

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