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Essential Statistics: Exploring the World through Data

Robert Gould, Colleen Ryan, Rebecca Wong

Chapter 1

Introduction to Data - all with Video Answers

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Chapter Questions

00:26

Problem 1

In Table $1 A$, how many variables are there?

Nick Johnson
Nick Johnson
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00:19

Problem 2

In Table $1 \mathrm{~A}$, there are observations on how many people?

Nick Johnson
Nick Johnson
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00:54

Problem 3

Are the following variables, from Table $1 \mathrm{~A}$, numerical or categorical? Explain.
a. Living situation
b. Commute distance
c. Number of aunts

Sheryl Ezze
Sheryl Ezze
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00:51

Problem 4

Are the following variables, from Table $1 \mathrm{~A}$, numerical or categorical? Explain.
a. Ring size
b. Hair color
c. Height

Nick Johnson
Nick Johnson
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00:42

Problem 5

Give an example of another numerical variable we might have recorded for the students whose data are in Table $1 \mathrm{~A}$ ?

Nick Johnson
Nick Johnson
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00:36

Problem 6

Give an example of another categorical variable we might have recorded for the students whose data are in Table $1 \mathrm{~A}$ ?

Nick Johnson
Nick Johnson
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00:43

Problem 7

Coding What do the numbers 1 and 0 mean for the variable Female, in Table 1 A (which is coded categorical data)? Often, it does not make sense, or is not even possible, to add a categorical variable. Does it make sense for Female? If so, what does the sum represent?

Nick Johnson
Nick Johnson
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00:32

Problem 8

Coding Suppose you decided to code living situation using Dorm as the label for the column. How many ones and how many zeroes would there be?

Nick Johnson
Nick Johnson
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00:24

Problem 9

Coding Explain why the variable Female, in Table $1 \mathrm{~A}$, is categorical, even though its values are numbers. Often, it does not make sense, or is not even possible, to add the values of a categorical variable. Does it make sense for Male? If so, what does the sum represent?

Nick Johnson
Nick Johnson
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01:22

Problem 10

Coding Students who have accumulated fewer than 30 units are called Freshmen.
a. Create a new categorical variable, named Freshman, that classifies each student in Table $1 \mathrm{~A}$ as a freshman (less than 30 units) or not a freshman. Call this variable Freshman. Report the coded values in a column in the same order as those in the table.
b. Was the original variable (college units) numerical or categorical?
c. Is your new coded column (Freshman) from part a numerical or categorical?

Nick Johnson
Nick Johnson
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01:39

Problem 11

A student shared data from the StatCrunch Friend Data Application. Data on gender and number of wall posts for a sample of friends are shown below. (Source: StatCrunch, Facebook Friend Data, posted $2 / 13 / 14$ )
a. Is the format of this data set stacked or unstacked?
b. Explain the coding. What do 1 and 0 represent?
c. If you answered "stacked" in part a, then unstack the data into two columns labeled Male and Female. If you answered "unstacked," then stack the data into one column and choose a appropriate name for the stacked variable.

Akhil Choudhary
Akhil Choudhary
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01:39

Problem 12

Age of Marriage A student did a survey on the age of marriage for married male and female students.
a. Is the format of the data set stacked or unstacked?
b. If you answered "stacked" then unstack the data into two columns. If you answered "unstacked" then stack the data into one column; choose an appropriate name for the stacked variable and use coding.
c. There are two variables here: Gender and $A g e$. Which of them is numerical, and which is categorical?

Akhil Choudhary
Akhil Choudhary
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01:05

Problem 13

Snacks Emmanuel, a student at a Los Angeles high school, kept track of the calorie content of all the snacks he ate for one week. He also took note of whether the snack was mostly "sweet" or "salty." The sweet snacks: $90,310,500,500,600,90$
The salty snacks: $150,600,500,550$
Write these data as they might appear in (a) stacked format with codes and (b) unstacked format.

Nick Johnson
Nick Johnson
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01:20

Problem 14

Movies A sample of students were questioned to determine how much they would be willing to pay to see a movie in a theater that served dinner at the seats. The male students responded (in dollars): $10,15,15,25$, and $12 .$ The female students responded: 8,30, 15, and $15 .$ Write these data as they might appear in (a) stacked format with codes and (b) unstacked format.

Nick Johnson
Nick Johnson
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00:12

Problem 15

Investigating Data (Example 3) Suppose you wanted to know whether living situation was associated with number of units the student had acquired. Could you do that with this data table? If so, which variables would you use?

Nick Johnson
Nick Johnson
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00:23

Problem 16

Investigating Data Suppose you wanted to know whether the men or the women tended to be taller. Could you do that with this data table? If so, which variables would you use?

Nick Johnson
Nick Johnson
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00:21

Problem 17

Investigating Data Suppose you wanted to know whether living situation was associated with number of hours of study per week. Could you do that with this data table? If so, which variables would you use?

Nick Johnson
Nick Johnson
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00:21

Problem 18

Investigating Data Suppose you wanted to know whether ring size and height were associated. Could you do that with this data table? If so, which variables would you use?

Nick Johnson
Nick Johnson
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01:21

Problem 19

Investigating Data (Example 4) A data set on Shark Attacks Worldwide posted on StatCrunch records data on all shark attacks in recorded history including attacks before $1800 .$ Variables contained in the data include time of attack, date, location, activity the victim was engaged in when attacked, type of injuries sustained by the victim, whether or not the injury was fatal, and species of shark. Which of the following questions could not be answered using this data set? (Source: www.sharkattackfile.net)
a. In what month do most shark attacks occur?
b. Are shark attacks more likely to occur in warm temperature or cooler temperatures?
c. Attacks by which species of shark are more likely to result in a fatality?
d. What country has the most shark attacks per year?

Nick Johnson
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00:32

Problem 20

Investigating Data Suppose a surfer wanted to learn if surfing during a certain time of day made one less likely to be attacked by a shark. Using the Shark Attacks Worldwide data set, which variables could the surfer use in order to answer this question?

Nick Johnson
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02:14

Problem 21

Hands (Example 5) A survey was done of men's and women's hands to see if the ring finger appeared longer than the index finger or not. Yes means the ring finger is longer, and No means the ring finger appears shorter or the same length as the index finger. The students in this survey were not told the theory that men are more likely to have a longer ring finger than women due to more testosterone.
a. What percentage of the men said Yes?
b. What percentage of the women said Yes?
c. What percentage of the people who said Yes were men?
d. If a large group of 250 men had the same rate of responses as the men in this sample, how many men of the 250 would say yes?

Nick Johnson
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01:51

Problem 22

Hands-Biased A survey was done of men's and women's hands to see if the ring finger appeared longer than the index finger or not. Yes means the ring finger is longer, and No means the ring finger appears shorter or the same length as the index finger. The students in this survey were told the theory that men are more likely to have a longer ring finger than women because of additional testosterone.
a. What percentage of the men said No?
b. What percentage of the women said No?
c. What percentage of the people who said No were men?
d. If a large group of 600 men had the same rate of responses as the men in this sample, how many men of the 600 would say No?

Nick Johnson
Nick Johnson
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05:43

Problem 23

a. A statistics class is made up of 15 men and 23 women. What percentage of the class is male?
b. A different class has 234 students, and $64.1 \%$ of them are men. How
many men are in the class?
c. A different class is made up of $40 \%$ women and has 20 women in it. What is the total number of students in the class?

Willis James
Willis James
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03:45

Problem 24

a. A hospital employs 346 nurses, and $35 \%$ of them are male. How many male nurses are there?
b. An engineering firm employs 178 engineers, and 112 of them are male. What percentage of these engineers are female?
c. A large law firm is made up of $65 \%$ male lawyers, or 169 male lawyers. What is the total number of lawyers at the firm?

Anna D.
Anna D.
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00:55

Problem 25

Find the frequency, proportion, and percentage of women in Table $1 \mathrm{~A}$ on page 31 .

Nick Johnson
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00:42

Problem 26

Find the frequency, proportion, and percentage of brown-haired people in Table $1 \mathrm{~A}$ on page 31 .

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02:29

Problem 27

Make a two-way table from Table 1 A for gender and living situation. Put the labels Male and Female across the top and Dorm and Commuter on the side and then tally the data. See page 38 for guidance.
a. Report how many are in each cell.
b. Find the sums for each column and row and the grand total and put them into your table. The grand total is the total number of people and is put in the lower right corner.
c. What percentage of the females live in a dorm?
d. What percentage of the people living in a dorm are female?
e. What percentage of people live in a dorm?
$\mathrm{f}_{\mathrm{t}}$ If the distribution of females remained roughly the same and you had 70 females, how many of them would you expect to be living in the dorm?

Nick Johnson
Nick Johnson
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02:07

Problem 28

Data Make a two-way table from Table I for gender and hair color. Put the labels Male and Female across the top and Brown, Black, Blonde, and Red and then tally the data.
a. Report how many are in each cell.
b. Find the sums of each row and column and the grand total and put them into your table.
c. What percentage of the females have brown hair?
d. What percentage of the people who have brown hair are female?
e. What percentage of the people have brown hair?
$\mathrm{f}$. If the distribution of hair color of females remained roughly the same and you had 60 females, how many of them would have brown hair?

Nick Johnson
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01:14

Problem 29

The 2017 World Almanac and Book of Facts reported that the U.S. occupation projected to grow the most is personal care aide. By 2024 there will be a need for 160,328 personal care aides, a growth of about $26 \%$ over 2014 levels. How many personal care aides were there in 2014 ?

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00:30

Problem 30

The 2017 World Almanac and Book of Facts reported that in $2016, \mathrm{M\&Ms}$ had sales of approximately $\$ 3.48$ million and that this accounted for $12.95 \%$ of the total chocolate candy sales. What was the total amount of chocolate candy sales?

Nick Johnson
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01:45

Problem 31

Incarceration Rates (Example 7) The table gives the prison population and total population for a sample of states in 2014-15. (Source: The 2017 World Almanac and Book of Facts)
$$
\begin{array}{|l|c|c|}
\hline \text { State } & \text { Prison Population } & \text { Total Population } \\
\hline \text { California } & 136,088 & 39,144,818 \\
\hline \text { New York } & 52,518 & 19,795,791 \\
\hline \text { Illinois } & 48,278 & 12,859,995 \\
\hline \text { Louisiana } & 38,030 & 4,670,724 \\
\hline \text { Mississippi } & 18,793 & 2,992,333 \\
\hline
\end{array}
$$
Find the number of people in prison per thousand residents in each state and rank each state from the highest rate (rank 1$)$ to the lowest rank (rank 6). Compare these rankings of rates with the ranks of total numbers of people in prison. Of the states in this table, which state has the highest prison population? Which state has the highest rate of imprisonment? Explain why these two answers are different.

James Kiss
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01:40

Problem 32

Population Density The accompanying table gives the 2018 population and area (in square kilometers) of five U.S. cities. See page 39 for guidance. (Source: www.citymayors.com).
$$
\begin{array}{l|c|c}
\text { City } & \text { Population } & \text { Area (square km) } \\
\hline \text { Miami } & 4,919,000 & 2891 \\
\hline \text { Detroit } & 3,903,000 & 3267 \\
\hline \text { Atlanta } & 3,500,000 & 5083 \\
\hline \text { Seattle } & 2,712,000 & 1768 \\
\hline \text { Baltimore } & 2,076,000 & 1768 \\
\hline
\end{array}
$$
a. Determine and report the ranking of the population density (people per square kilometer) by dividing the population of each city by its area. Use rank 1 for the highest density.
b. If you wanted to live in the city (of these six) with the lowest population density, which would you choose?
c. If you wanted to live in the city (of these six) with the highest population density, which would you choose?

Nick Johnson
Nick Johnson
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01:49

Problem 33

Health Insurance The accompanying table gives the population (in hundred thousands) and number of people not covered by health insurance (in hundred thousands) for the United States. Find the percentage of people not covered by health insurance for each of the given years and describe the trend. (Source: 2017 World Almanac and Book of Facts $)$
$$
\begin{array}{|c|c|c|}
\hline \text { Year } & \text { Uninsured } & \text { Total Population } \\
\hline 1990 & 34,719 & 249,778 \\
\hline 2000 & 36,586 & 279,282 \\
\hline 2015 & 29,758 & 316,574 \\
\hline
\end{array}
$$

Nick Johnson
Nick Johnson
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02:41

Problem 34

The accompanying table gives the number of cable television subscribers (in millions) and the number of households with televisions (in millions) in the United States. Find the percentage of TV owners with cable subscriptions for each year and comment on the trend over time. (Source: 2017 World Almanac and Book of Facts)

Nick Johnson
Nick Johnson
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01:40

Problem 35

The projected U.S. population is given for different decades. The projected number of people 65 years of age or older is also given. Find the percentage of people 65 or over and comment on the trend over time. Numbers are in millions of people (Source: 2017 World Almanac and Book of Facts)
$$
\begin{array}{|c|c|c|}
\hline \text { Year } & \text { Population } & \text { Older Population } \\
\hline 2020 & 334 & 54.8 \\
\hline 2030 & 358 & 70.0 \\
\hline 2040 & 380 & 81.2 \\
\hline 2050 & 400 & 88.5 \\
\hline
\end{array}
$$

Nick Johnson
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01:45

Problem 36

The marriage and divorce rates are given per 1000 people in various years. Find the divorce rate as a percentage of the marriage rate and comment on the trend over time. (Source: https://www.cdc.gov/nchs)
$$
\begin{array}{|c|c|c|}
\hline \text { Year } & \text { Marriage } & \text { Divorce } \\
\hline 2000 & 8.2 & 4.0 \\
\hline 2005 & 7.6 & 3.6 \\
\hline 2010 & 6.8 & 3.6 \\
\hline 2014 & 6.9 & 3.2 \\
\hline
\end{array}
$$

Nick Johnson
Nick Johnson
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00:42

Problem 37

Two sections of statistics are offered, the first at 8 a.m. and the second at 10 a.m. The 8 a.m. section has 25 women, and the 10 a.m. section has 15 women. A student claims this is evidence that women prefer earlier statistics classes than men do. What information is missing that might contradict this claim?

Nick Johnson
Nick Johnson
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00:57

Problem 38

In 2015, the National Highway Traffic Safety Administration reported the number of pedestrian fatalities in San Francisco County was 24 and that the number in Los Angeles County was 209. Can we conclude that pedestrians are safer in San Francisco than in Los Angeles? Why or why not? If you answered no, what additional data would allow us to make a conclusion about which county is safer for pedestrians? (Source: https://cdan.nhtsa.gov)

Nick Johnson
Nick Johnson
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00:31

Problem 39

Indicate whether the study is an observational study or a controlled experiment.
Patients with high blood pressure are asked to keep food diaries recording all items they eat for a one-week period. Researchers analyze the food diary data for trends.

Nick Johnson
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00:32

Problem 40

Indicate whether the study is an observational study or a controlled experiment.
Patients with multiple sclerosis are randomly assigned a new drug or a placebo and are then given a test of coordination after six months.

Nick Johnson
Nick Johnson
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00:38

Problem 41

Indicate whether the study is an observational study or a controlled experiment.
A researcher is interested in the effect of music on memory. She randomly divides a group of students into three groups: those who will listen to quiet music, those who will listen to loud music, and those who will not listen to music. After the appropriate music is played (or not played), she gives all the students a memory test.

Nick Johnson
Nick Johnson
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00:17

Problem 42

Indicate whether the study is an observational study or a controlled experiment.
Patients with Alzheimer's disease are randomly divided into two groups. One group is given a new drug, and the other is given a placebo. After six months they are given a memory test to see whether the new drug fights Alzheimer's better than a placebo.

Nick Johnson
Nick Johnson
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00:19

Problem 43

Indicate whether the study is an observational study or a controlled experiment.
A group of boys is randomly divided into two groups. One group watches violent cartoons for one hour, and the other group watches cartoons without violence for one hour. The boys are then observed to see how many violent actions they take in the next two hours, and the two groups are compared.

Nick Johnson
Nick Johnson
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00:41

Problem 44

Indicate whether the study is an observational study or a controlled experiment.
A local public school encourages, but does not require, students to wear uniforms. The principal of the school compares the grade point averages (GPAs) of students at this school who wear uniforms with the GPAs of those who do not wear uniforms to determine whether those wearing uniforms tend to have higher GPAs.

Nick Johnson
Nick Johnson
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01:46

Problem 45

The blog $N H S$ Choices (February 10, 2014 ) noted that "there has been increasing anecdotal evidence that vitamin C may still be useful as an anticancer medicine if used in high concentrations and given directly into the vein (intravenously)." Explain what it means that there is "increasing anecdotal evidence" that Vitamin C may be a useful anticancer medicine. How does anecdotal evidence contrast with scientific evidence? What kind of conclusions, if any, can be made from anecdotal evidence?

Nick Johnson
Nick Johnson
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00:42

Problem 46

You can find many testimonials on the Internet that drinking aloe vera juice helps with digestive ailments. From these testimonials can we conclude that aloe vera juice causes digestive problems to go away? Why or why not?

Nick Johnson
Nick Johnson
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01:01

Problem 47

Effects of Tutoring on Math Grades (Example 8) A group of educators want to determine how effective tutoring is in raising students' grades in a math class, so they arrange free tutoring for those who want it. Then they compare final exam grades for the group that took advantage of the tutoring and the group that did not. Suppose the group participating in the tutoring tended to receive higher grades on the exam. Does that show that the tutoring worked? If not, explain why not and suggest a confounding variable.

Nick Johnson
Nick Johnson
Numerade Educator
02:21

Problem 48

A doctor who believes strongly that antidepressants work better than "talk therapy" tests depressed patients by treating half of them with antidepressants and the other half with talk therapy. After six months the patients are evaluated on a scale of 1 to 5 , with 5 indicating the greatest improvement.
a. The doctor is concerned that if his most severely depressed patients do not receive the antidepressants, they will get much worse. He therefore decides that the most severe patients will be assigned to receive the antidepressants. Explain why this will affect his ability to determine which approach works best.
b. What advice would you give the doctor to improve his study?
c. The doctor asks you whether it is acceptable for him to know which treatment each patient receives and to evaluate them himself at the end of the study to rate their improvement. Explain why this practice will affect his ability to determine which approach works best.
d. What improvements to the plan in part c would you recommend?

Nick Johnson
Nick Johnson
Numerade Educator
00:47

Problem 49

In a 2017 study designed to investigate the effects of exercise on secondlanguage learning, 40 subjects were randomly assigned to one of two conditions: an experimental group that engaged in simultaneous physical activity while learning vocabulary in a second language and a control group that learned the vocabulary in a static learning environment. Researchers found that learning second-language vocabulary while engaged in physical activity led to higher performance than learning in a static environment. (Source: Liu et al., "It takes biking to learn: Physical activity improves learning a second language," PLoS One, May 18,2017, https://doi.org/10.1371/journal. pone.0177624)
a. What features of a well-designed controlled experiment does this study have? Which features are missing?
b. Assuming that the study was properly conducted, can we conclude that the physical activity while learning caused the higher performance in learning second-language vocabulary? Explain.

Nick Johnson
Nick Johnson
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00:50

Problem 50

A study reported by Griffin et al. compared the rate of pneumonia between 1997 and 1999 before pneumonia vaccine (PCV7) was introduced and between 2007 and 2009 after pneumonia vaccine was introduced. Read the excerpts from the abstract, and answer the question that follows it. (Source: Griffin et al., "U.S. hospitalizations for pneumonia after a decade of pneumococcal vaccination," New England Journal of Medicine, vol. $369[$ July 11,201$]: 155-163$ )
We estimated annual rates of hospitalization for pneumonia from any cause using the Nationwide Inpatient Sample database..... Average annual rates of pneumonia-related hospitalizations from 1997 through 1999 (before the introduction of PCV7) and from 2007 through 2009 (well after its introduction) were used to estimate annual declines in hospitalizations due to pneumonia.

The annual rate of hospitalization for pneumonia among children younger than 2 years of age declined by $551.1$ per 100,000 children $\ldots$ which translates to 47,000 fewer hospitalizations annually than expected on the basis of the rates before PCV7 was introduced.
Results for other age groups were similar. Does this show that pneumonia vaccine caused the decrease in pneumonia that occurred? Explain.

Nick Johnson
Nick Johnson
Numerade Educator
01:30

Problem 51

Does Fish Oil Lower Asthma Risk? The New England Journal of Medicine reported on a study of fish oil consumption in pregnant mothers and the subsequent development of asthma in their children. Read the excerpts from the abstract and answer the questions that follow: (Source: Bisgaard et al., "Fish oil-derived fatty acids in pregnancy and wheeze and asthma in offspring,"
New England Journal of Medicine, vol. 375 [December 2016]:
2530-2539, doi: 10.1056/NEJMoa1503734
Methods: We randomly assigned 736 pregnant women at 24 weeks of gestation to receive fish oil or a placebo (olive oil) daily. Neither the investigators nor the participants were aware of group assignments during follow-up for the first 3 years of the children's lives, after which there was a 2 -year follow-up period during which only the investigators were unaware of group assignments.

Results: A total of 695 children were included in the trial, and $95.5 \%$ completed the 3-year, double-blind follow-up period. The risk of persistent wheeze or asthma in the treatment group was $16.9 \%$, versus $23.7 \%$ in the control group, corresponding to a relative reduction of $30.7 \%$.
a. Was this a controlled experiment or an observational study? Explain how you know.
b. Assuming the study was properly conducted, can we conclude that the lower rate of asthma was caused by the mother's consumption of fish oil?

Nick Johnson
Nick Johnson
Numerade Educator
01:35

Problem 52

Association between Glycemic Load and Acne? An article in the Journal of the Academy of Nutrition and Dietetics reported on a study of diet in subjects with moderate to severe acne. Read the excerpts from the abstract and answer the questions that follow. (Source: Burris et al., "Differences in dietary glycemic load and hormones in New York City adults with no or moderate/severe acne," Journal of the Academy of Nutrition and Dietetics, vol. 117 [September 2017]: $1375-1383$ )

Methods: Sixty-four participants (no acne, $\mathrm{n}=32$; moderate/severe acne, $\mathrm{n}=32$ ) were included in this study. Participants completed a 5 -day food record, had blood drawn and completed a questionnaire to evaluate food-aggravated acne beliefs and acne-specific quality of life.
Results: Participants with moderate/severe acne consumed greater total carbohydrate compared to participants without acne. Participants with moderate/severe acne had greater insulin compared to participants without acne. Although there were no differences between groups, $61 \%$ of participants reported food-influenced acne.
a. Was this a controlled experiment or an observational study? Explain how you know.
b. Assuming the study was properly conducted, can we conclude that higher consumption of carbohydrates causes more severe acne? Explain.

Nick Johnson
Nick Johnson
Numerade Educator
00:39

Problem 53

Milk and Cartilage (Example 10) Cartilage is a smooth, rubber-like padding that protects the long bones in the body at the joints. A study by Lu et. al. in Arthritis Care \& Research found that women who drank one glass of milk daily had $32 \%$ thicker, healthier cartilage than women who did not. Researchers obtained information on milk consumption through questionnaires and measured cartilage through x-rays. In the article, researched conclude, "Our study suggested that frequent milk intake may be associated with reduced OA progression in women." (Source: Lu et al., "Milk consumption and progression of medial tibiofemoral knee osteoarthritis: Data from the osteoarthritis initiative," Arthritis Care \& Research, vol. 66 [June 2014]: 802-809, https://doi.org/10.10002/acr.22297
Does this study show drinking milk causes increased cartilage production? Why or why not?

Nick Johnson
Nick Johnson
Numerade Educator
00:48

Problem 54

An article by Wakefield et al. in the British medical journal Lancet claimed that autism was caused by the measles, mumps, and rubella (MMR) vaccine. This vaccine is typically given to children twice, at about the age of 1 and again at about 4 years of age. In the article 12 children with autism who had all received the vaccines shortly before developing autism were studied. The article was later retracted by Lancet because the conclusions were not justified by the design of the study.
Can you conclude that the MMR vaccine causes Autism from this study? Explain why Lancet might have felt that the conclusions (MMR causes autism) were not justified by listing potential flaws in the study, as described above. (Source: A. J. Wakefield et al., "Ileal lymphoid-nodular hyperplasia, non-specific colitis, and pervasive developmental disorder in children." Lancet, vol. 351 (February $1998): 637-641$ )

Nick Johnson
Nick Johnson
Numerade Educator
01:52

Problem 55

Diet and Depression (Example 11) An article in the journal BMC Medicine reported on a study designed to study the effect of diet on depression. Subjects suffering from moderate to severe depression were randomly assigned to one of two groups: a diet intervention group and a social support control group. The 33 subjects in the diet intervention group received counseling and support to adhere to a "ModiMedDiet," based primarily on a Mediterranean diet. The 34 subjects in the social support group participated in a "befriending" protocol, where trained personnel engaged in conversation and activities with participants. At the end of a 12 -week period, 11 of the diet intervention group achieved remission from depression compared to 3 of the control group.
$$
\begin{array}{|l|c|c|}
\hline & \begin{array}{c}
\text { Diet } \\
\text { (Intervention) }
\end{array} & \begin{array}{c}
\text { Support } \\
\text { (Control) }
\end{array} \\
\hline \text { Remission } & 11 & 3 \\
\hline \text { No Remission } & 22 & 31 \\
\hline
\end{array}
$$
a. Find and compare the sample percentage of remission for each group.
b. Was this a controlled experiment or an observational study? Explain.
c. Can we conclude that the diet caused a remission in depression? Why
or why not?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:10

Problem 56

A study was conducted to see whether participants would ignore a sign that said, "Elevator may stick between floors. Use the stairs." The study was done at a university dorm on the ground floor of a three-level building. Those who used the stairs were said to be compliant, and those who used the elevator were said to be noncompliant. There were three possible situations, two of which involved confederates. A confederate is a person who is secretly working with the experimenter. In the first situation, there was no confederate. In the second situation, there was a compliant confederate (one who used the stairs), and in the third situation, there was a noncompliant confederate (one who used the elevator). The subjects tended to imitate the confederates. What more do you need to know about the study to determine whether the presence or absence of a confederate causes a change in the compliance of subjects? (Source: Wogalter et al. [1987], reported in Shaffer and Merrens, Research Stories in Introductory Psychology [Boston: Allyn and Bacon, 2001])

Nick Johnson
Nick Johnson
Numerade Educator
00:30

Problem 57

A Salad a Day Keeps Stroke Away? The Harvard Heart Letter reported on a study that examined the diets of 1226 older women over 15 years. They discovered that the more vegetables the women consumed, the lower their risk of dying of cardiovascular disease. From this study can we conclude that eating a diet high in vegetables prevents cardiovascular disease? Why or why not?

Nick Johnson
Nick Johnson
Numerade Educator
00:52

Problem 58

Does Drinking Sugary Beverages Lead to Dementia? The September 2017 issue of Alzheimer's and Dementia reported on a study that found an association between drinking sugary drinks and lower brain volume. Is this likely to be a conclusion from observational studies or randomized experiments? Can we conclude that drinking sugary beverages causes lower brain volume? Why or why not?

Nick Johnson
Nick Johnson
Numerade Educator
01:03

Problem 59

$1.59$ Secondhand Smoke Exposure and Young Children Researchers wanted to assess whether a theory-based, community health worker-delivered intervention for household smokers will lead to reduced secondhand smoke exposure to children in Chinese families. Smoking parents or caregivers who had a child aged 5 years or younger at home were randomly assigned to the intervention group that received information on smoking hygiene and the effects of secondhand smoke exposure delivered by community health workers or to the comparison group who received no additional information regarding secondhand smoke. At a 6-month follow-up, researchers assessed whether or not families had adopted any smoking restrictions at home. The results are shown in the following table. (Source: Abdullah et al., "Secondhand smoke exposure reduction intervention in Chinese households of young children:
A randomized controlled trial," Academic Pediatrics, vol. 15 (November-December 2015): $588-598$, https://doi.org/10.1016/j. acap. $2015.06 .008$ )$$
\begin{array}{|l|c|c|}
\hline & \text { Intervention } & \text { Control } \\
\hline \text { Smoking Restrictions } & 61 & 37 \\
\hline \text { No restrictions } & 37 & 45 \\
\hline \text { Total } & 98 & 82 \\
\hline
\end{array}
$$
a. What percentage of those receiving the intervention adopted smoking restrictions at home?
b. What percentage of those in the control group adopted smoking restrictions at home?
c. Based on this data, do you think the intervention may have been effective in promoting the adoption of smoking restrictions in the home?

Nick Johnson
Nick Johnson
Numerade Educator
01:07

Problem 60

Coffee Consumption The August 27,2017, issue of Science Daily reported that higher coffee consumption is associated with a lower risk of death. This was based on an observational study of nearly 20,000 participants. Researchers found that participants who consumed at least 4 cups of coffee per day had a $64 \%$ lower risk of mortality than those who never or almost never consumed coffee. Does this mean that a person can reduce his or her chance of death by increasing the amount of coffee consumed?

James Kiss
James Kiss
Numerade Educator
01:54

Problem 61

Speeding Tickets College students who were drivers were asked if they had ever received a speeding ticket (yes or no). The results are shown in the table, along with gender.
a. There are two variables in the table, state what they are and whether each is categorical or numerical.
b. Make a two-way table of the results with Male and Female across the top and Yes and No at the left edge.
c. Compare the percentages of men and women who have received speeding tickets.
$$
\begin{array}{|c|c|c|c|}
\hline \text { Gender } & \text { Ticket } & \text { Gender } & \text { Ticket } \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{y} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{y} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{f} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{f} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{f} & \mathrm{y} & & \\
\hline
\end{array}
$$

Nick Johnson
Nick Johnson
Numerade Educator
01:42

Problem 62

College students who were drivers were asked if they had ever driven a car 100 mph or more (yes or no). The results are shown in the table, along with gender.
a. There are two variables in the table, state what they are and whether each is categorical or numerical.
b. Make a two-way table of the results with Male and Female across the top and Yes and No at the left edge.
c. Compare the percentages of men and women who have driven $100 \mathrm{mph}$
or more.
$$
\begin{array}{|c|c|c|c|}
\hline \text { Gender } & \mathbf{1 0 0}+\text { mph } & \text { Gender } & \mathbf{1 0 0}+\mathbf{~ m p h} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{y} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{y} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{f} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{f} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline \mathrm{f} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\
\hline
\end{array}
$$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:14

Problem 63

Describe the design of a controlled experiment to determine whether the use of vitamin D supplements reduces the chance of broken bones in women with osteoporosis (weak bones). Assume you have 200 women with osteoporosis to work with. Your description should include all the features of a controlled experiment. Also decide how the results would be determined.

Nick Johnson
Nick Johnson
Numerade Educator
01:01

Problem 64

Writing: Strokes People who have had strokes are often put on "blood thinners" such as aspirin or Coumadin to help prevent a second stroke. Describe the design of a controlled experiment to determine whether aspirin or Coumadin works better in preventing second strokes. Assume you have 300 people who have had a first stroke to work with. Include all the features of a good experiment. Also decide how the results would be determined.

Nick Johnson
Nick Johnson
Numerade Educator
01:45

Problem 65

Yoga and High-Risk Adolescents Can mindful yoga have a beneficial impact on alcohol use in high-risk adolescents? Read excerpts from the research published in The Journal of Child and Family Studies and answer the questions that follow. (Source: Fishbein et al., "Behavioral and psychophysiological effects of a yoga intervention on high-risk adolescents: A randomized control trial," Journal of Child and Family Studies, vol. 25 [February 2016]:
518-529, https://doi.org/10.1007/s10826-015-0231-6)

Abstract: We designed a 20-session mindful yoga intervention for adolescents attending a school for students at high risk of dropping out, The 69 participants were randomly assigned to control and intervention groups. Survey data were collected before and after the yoga curriculum. At the post test, students in the yoga condition exhibited trends toward decreased alcohol use as compared to control students.
a. Identify the treatment variable and the response variable.
b. Was this a controlled experiment or an observational study?
c. Based on this study, can you conclude that yoga caused a decrease in alcohol use? Why or why not?

Nick Johnson
Nick Johnson
Numerade Educator
01:47

Problem 66

Some studies have indicated that neurofeedback may be an effective treatment for ADHD. Read excerpts from the research published in The Lancet Psychiatry and answer the questions that follow. (Source: Schönenberg et al., "Neurofeedback, sham neurofeedback, and cognitive-behavioral group therapy in adults with attention-deficit hyperactivity disorder: A triple-blind, randomised, controlled trial, "The Lancet Psychiatry, vol. 4 [September 2017]: $673-684$ )

Methods: We did a concurrent, triple-blind, randomised, controlled trial using adults with ADHD, aged 18 to 60 years. Participants were randomly assigned to three groups: a neurofeedback group which received 30 true neurofeedback sessions over 15 weeks, a sham neurofeedback group which received 15 sham (fake) followed by 15 true neurofeedback sessions over 15 weeks, or a meta-cognitive group therapy group which received 12 sessions over 12 weeks. The primary outcome was symptom score on the Conners' adult ADHD rating scale, assessed before treatment, at midtreatment (after 8 weeks), after treatment (after 16 weeks), and 6 months later.

Results: Self-reported ADHD symptoms decreased substantially for all treatment groups between pretreatment and the end of 6 month follow-up, independent of treatment condition. There were no significant differences in outcomes between any of the groups.
a. Identify the treatment variable and the response variable.
b. Was this a controlled experiment or an observational study?
c. Based on this study, would you agree that neurofeedback may be an effective treatment for ADHD? Why or why not?

Nick Johnson
Nick Johnson
Numerade Educator
01:40

Problem 67

Virtual Reality and Fall Risk A study was conducted to assess whether 5 weeks of training with virtual reality (VR) can reduce the risk of falls in adults. Thirty-four older adults underwent 15 VR training sessions consisting of walking on a treadmill with a VR simulation. At the end of the VR training program, participants showed improved mobility and gait speed. In the abstract the authors conclude that "[t]readmill training with VR appears to be an effective and practical clinical tool to improve mobility and reduce falls in older adults." Do these results indicate that VR training can cause improvement in mobility and gait speed among older adults? What essential component of both controlled experiments and observational studies is missing from this study? (Source: Shema et al., "Improved mobility and reduced fall risk in older adults after five weeks of virtual reality training," Journal of Alternative Medical Research, $9(2), 171-175 .)$

Nick Johnson
Nick Johnson
Numerade Educator
View

Problem 68

Ear Infections Babies 6 to 23 months of age with inner ear infections were given antibiotics. The children were randomly assigned to receive antibiotics for a full 10 days or to receive antibiotics for 5 days and then a placebo for 5 days. There were 229 children assigned the shorter course, and 77 of them had "clinical failure" whereas of the 238 assigned to the longer course of antibiotics, 39 had clinical failure. (Source: Hoberman et al., "Shortened antimicrobial treatment for acute otitis media in young children," New England Journal of Medicine, vol. 375 [December 2016]:
$2446-2456)$
a. Compare the percentage of clinical failure in each group and state which group did better.
b. Create a two-way table with 10 days and 5 days across the top and failure and success down the left side. Fill in all four numbers.
c. Was this an observational study or a controlled experiment? How do you know?
d. Can you conclude that the treatment caused the difference? Why or why not?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:28

Problem 69

$1.69$ Effects of Light Exposure A study carried out by Baturin and colleagues looked at the effects of light on female mice. Fifty mice were randomly assigned to a regimen of 12 hours of light and 12 hours of dark (LD), while another 50 mice were assigned to 24 hours of light (LL). Researchers observed the mice for two years, beginning when the mice were 2 months old. Four of the LD mice and 14 of the LL mice developed tumors. The accompanying table summarizes the data. (Source: Baturin et al., "The effect of light regimen and melatonin on the development of spontaneous mammary tumors in mice," Neuroendocrinology Letters, vol. 22 [December 2001]: $441-447$ )
$$
\begin{array}{|l|r|r|}
\hline & \text { LD } & \text { LL } \\
\hline \text { Tumors } & 4 & 14 \\
\hline \text { No tumors } & 46 & 36 \\
\hline
\end{array}
$$
a. Determine the percentage of mice that developed tumors from each group (LL and LD). Compare them and comment.
b. Was this a controlled experiment or an observational study? How do you know?
c. Can we conclude that light for 24 hours a day causes an increase in tumors in mice? Why or why not?

Nick Johnson
Nick Johnson
Numerade Educator
01:10

Problem 70

Scared Straight The idea of sending delinquents to "Scared Straight" programs has appeared recently in several media programs (such as Dr. Phil) and on a program called Beyond Scared Straight. So it seems appropriate to look at a randomized experiment from the past. In 1983 , Roy Lewis reported on a study in California. Each male delinquent in the study (all were aged $14-18$ ) was randomly assigned to either Scared Straight or no treatment. The males who were assigned to Scared Straight went to a prison, where they heard prisoners talk about their bad experiences there. Then the males in both the experimental and the control group were observed for 12 months to see whether they were rearrested. The table shows the results. (Source: Lewis, "Scared straight - California style: Evaluation of the San Quentin Squires program," Criminal Justice and Behavior, vol. 10 [June 1983]: 209-226)
$$
\begin{array}{|c|c|c|}
\hline & \text { Scared Straight } & \text { No Treatment } \\
\hline \text { Rearrested } & 43 & 37 \\
\hline \text { Not rearrested } & 10 & 18 \\
\hline
\end{array}
$$
a. Report the rearrest rate for the Scared Straight group and for the No Treatment group, and state which is higher.
b. This experiment was done in the hope of showing that Scared Straight would cause a lower arrest rate. Did the study show that? Explain.

Nick Johnson
Nick Johnson
Numerade Educator