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theory of statistics
Statistics For The Behavioral Sciences 5th Edition Susan A Nolan, Thomas Heinzen - Solutions
Explain what is meant by unimodal, bimodal, and multimodal distributions.
Explain how the mean mathematically balances the distribution.
The mean can be assessed visually and arithmetically. Describe each method.
Dene the three measures of central tendency: mean, median, and mode.
Identifying variables and the best graph: For each of the following studies, list (i) the independent variable or variables and how they were operationalized, (ii) the dependent variable or variables and how they were operationalized, and (iii) the ideal type of graph that would depict these data.
Developing research questions from graphs: Graphs not only answer research questions but can also spur new ones.Figure 3-5 depicts the pattern of changing attitudes, as expressed through Twitter.
Type of graph describing the effect of romantic songs on ratings of attractiveness: Guéguen, Jacob, and Lamy (2010)wondered if listening to romantic songs would affect the dating behavior of the French heterosexual women who participated in their study. The women were randomly assigned to listen
Comparing word clouds and subjective well-being: Social science researchers are increasingly using word clouds to convey their results. A research team from the Netherlands asked 66 older adults to generate a list of what they perceive to be important to their well-being (Douma et al., 2015). Based
Word clouds and statistics textbooks: The Web site Wordle lets you create your own word clouds (wordle.net/create). (There are a number of other online tools to create word clouds, including TagCrowd and WordItOut.) Here’s a word cloud we made with the main text from this chapter. In your own
Critiquing a graph about gun deaths: In this chapter, we learned about graphs that are designed to be unclear. Think about the problems in the graph shown here.
Interpreting a graph about trafc ow: Go to maps.google.com. On a map of your country, select “Trafc” from the drop-down menu in the upper le corner.a. How is the density and ow of trafc represented in this graph?b. Describe trafc patterns in different regions of your country.c. What are the
Thinking critically about a graph of international students: Researchers surveyed Canadian students on their perceptions of the globalization of their campuses (Lambert &Usher, 2013). The 13,000 participants were domestic undergraduate and graduate students—that is, they were not
Thinking critically about a graph of the frequency of psychology degrees: The American Psychological Association(APA) compiles many statistics about training and careers in the eld of psychology. The accompanying graph tracks the number of bachelor’s, master’s, and doctoral degrees conferred
Interpreting a graph about two kinds of career regrets:The Yerkes–Dodson graph demonstrates that graphs can be used to describe theoretical relations that can be tested. In a study that could be applied to the career decisions made during college, Gilovich and Medvec (1995) identied two types of
Graphs in the popular media: Find an article in the popular media (newspaper, magazine, Web site) that includes a graph in addition to the text.
Creating the perfect graph: What advice would you give to the creator of the following graph? Consider the basic guidelines for a clear graph, for avoiding chartjunk and regarding the ways to mislead through statistics. Give three pieces of advice. Be specic—don’t just say that there is
Soware defaults of graphing programs for depicting the“world’s deepest” trash bin: The car company Volkswagen has sponsored a “fun theory” campaign in recent years in which
Soware defaults of graphing programs and perceptions of health care advice: For this exercise, use the data in the pie chart from the Fitbit report in the previous exercise.a. Create a bar graph for these data. Play with the options available to you and make changes so that the graph meets the
Bar graph versus pie chart and perceptions of health care advice: The company that makes Fitbit, the wristband that tracks exercise and sleep, commissioned a report that included the pie chart shown here (Trajectory Group, 2013). Explain why a bar graph would be more suitable for these data than a
Bar graph versus time series plot of graduate school mentoring: Johnson et al. (2000) conducted a study of mentoring in two types of psychology doctoral programs: experimental and clinical. Students who graduated from the two types of programs were asked whether they had a faculty mentor while in
on the average number of years it takes students to complete a doctorate at 41 different universities.a. Construct a dot plot for these data.
Survey of Earned Doctorates and a dot plot: Use the data from Exercise
Consideration of Future Consequences and a dot plot: The following data are Consideration of Future Consequences (CFC)scores for 20 students, already arranged in order from lowest to highest:
Bar graph versus Pareto chart of countries’ gross domestic product: In How It Works 3.2, we created a bar graph for the 2012 GDP, in U.S. dollars per capita, for each of the G8 nations. More specically, we created a Pareto chart.
Bar graph of acceptance rates for different types of psychology doctoral programs: The American Psychological Association (Michalski et al., 2016) gathered data from almost 1000 psychology doctoral programs in the United States. (Note: If a school offered, say, four different psychology doctorates,
Time series plot of organ donations: The Canadian Institute for Health Information (CIHI) is a nonprot organization that compiles data from a range of institutions—from governmental organizations to hospitals to universities. Among the many topics that interest public health specialists is the
Scatterplot of gross domestic product and education levels: The Group of Seven (G7) consists of many of the major world economic powers. It meets annually to discuss pressing world problems. Here are 1 year’s data for gross domestic product (GDP) and a measure of education. The measure of
Scatterplot of daily cycling distances and type of climb:Every summer, the touring company America by Bicycle conducts the “Cross Country Challenge,” a 7-week bicycle journey across the United States from San Francisco, California, to
in the Philippines.
Type of graph for comparative suicide rates: The World Health Organization tracks suicide rates by gender across countries. For example, in 1 year, the rate of suicide per 100,000 men was 17.3 in Canada, 17.7 in the United States, 44.6 in Sri Lanka, 53.9 in the Russian Federation, 1.4 in South
Type of graph for the effects of cognitive-behavioral therapy on depression: A social worker tracked the depression levels of clients being treated with cognitive-behavioral therapy for depression. For each client, depression was assessed at weeks 1 to 20 of therapy. She calculated a mean for all
Graphing the relation between international researchers and the impact of research: Does research from international teams make a bigger splash? Researchers explored whether research conducted by multinational research teams had a bigger impact than research from teams with less international
Students in a statistics course reported the number of hours of sleep they get on a typical weeknight. These data appear below.5 6.5 6 8 6 6 6 7 5 7 6 6.5 7 6 7 4 8 6a. Create a dot plot of these data.b. Use the dot plot to describe the distribution of the set of scores.
a. Using the following set of data, construct a dot plot.
The scatterplot in How It Works 3.1 depicts the relation between fertility and life expectancy. Each dot represents a country.
If you had the following range of data for one variable, how might you label the relevant axis? 0.10 0.31 0.27 0.04 0.09 0.22 0.36 0.18
When creating a graph, we need to make a decision about the numbering of the axes. If you had the following range of data for one variable, how might you label the relevant axis?
The following gure presents the enrollment of graduate students at a university, across six fall terms, as a percentage of the total student population.
What elements are missing from the graphs in Exercises 3.22 and 3.23?
Do the data in the graph below show a linear relation, a nonlinear relation, or no relation? Explain.
You are exploring the relation between news source (online news Web sites versus social media) and knowledge about current affairs, as measured by scores on a test about world news.a. In this study, what are the independent and dependent variables?b. Is news source a nominal, ordinal, or scale
Alumni giving rates for a number of universities, calculated as the number of alumni who donated and the number who did not donate in a given year, represent which kind of variable—nominal, ordinal, or scale? What would be an appropriate graph to depict these data?
Alumni giving rates, calculated as the total dollars donated per year from 2010 to 2020, represent which kind of variable—nominal, ordinal, or scale? What would be an appropriate graph to depict these data?
What information does a violin plot depict?
Why is it important to show variability on a graph, rather than just presenting a bar graph?
Geographic information systems (GIS), such as those provided by computerized graphing technologies, are particularly powerful tools for answering what kinds of research questions?
Chartjunk comes in many forms. What specically are moiré vibrations, grids, and ducks?
Under what circumstances would the x-axis and y-axis not start at 0?
Why is it important to identify the independent variable and the dependent variable before creating a visual display?
Why are bar graphs preferred over pictorial graphs and pie charts?
What are pictorial graphs and pie charts?
In what way are dot plots similar to histograms?
What are potential benets of using a dot plot instead of a histogram?
Bar graphs and histograms look very similar. In your own words, what is the difference between the two?
What is the difference between a bar graph and a Pareto chart?
What is the difference between a line graph and a time plot?
How can we tell whether two variables are linearly or nonlinearly related?
What does it mean for two variables to be linearly related?
What does an individual dot on a scatterplot represent?
What are the steps to create a scatterplot?
What is a gure?
Frequencies, distributions, and graduate advising: In a study of mentoring in chemistry elds, a team of chemists and social scientists identied the most successful U.S. mentors—professors whose students were hired by the top 50 chemistry departments in the United States (Kuck et al., 2007).
Developing research ideas from frequency distributions:Below are frequency distributions for two sets of the friends data described in Exercise 2.38, one for the students and one for the faculty members studied.
Frequencies, distributions, and obesity around the world: The World Happiness Report publishes a number of indicators related to physical and psychological well-being(Helliwell et al., 2018). For example, it publishes adult obesity rates for more than 30 countries, with those percentages?
Frequencies, distributions, and numbers of friends: A college student is interested in how many friends the average person has. She decides to count the number of people who appear in photographs on display in dorm rooms and ofces across campus. She collects data on 84 students and 33 faculty
million people have the last name Smith, the most common name in this data set. So, Smith would be one of the seven names listed in the top row—last names that occur more than 1,000,000 times in the population. In another example, more than 72,000 people have the last name Singh. So, Singh is one
Skew and surname frequencies: Researchers published a summary of the frequency of surnames based on U.S. Census data (Word et al., 2008). The table lists the frequencies of last names in the le column, the number of last names with that level of frequency in the next column, and then the cumulative
Number of televisions and a grouped frequency distribution: The Canadian Radio-Television and Communications Commission (crtc.gc.ca/eng/publications)
Type of frequency distribution and type of graph: For each of the types of data described below, rst state how you would present individual data values or grouped data when creating a frequency distribution. Then, state which visual display(s) of data would be most appropriate to use. Explain your
Types of distributions: Consider these three variables:nishing times in a marathon, number of university dining hall meals eaten in a semester on a three-meal-a-day plan, and scores on a scale of extroversion.
Frequency tables, histograms, and basketball wins: Here are the number of wins for the 30 U.S. National Basketball Association (NBA) teams from a recent NBA season.
Frequency tables, histograms, and life expectancy rates:The United Nations Development Programme (2015) published life expectancy rates—the number of years an adult can expect to live—for 195 countries around the world. Following is a randomly selected sample of 30 of them.
Frequency tables, histograms, and the Survey of Earned Doctorates: The Survey of Earned Doctorates provides data on the length of time in years that it takes to complete a doctorate.Each data point is the mean time for one university. Following is a modied list of these completion-time data,
Frequency tables, histograms, and the National Survey of Student Engagement: The National Survey of Student Engagement (NSSE) surveys U.S. rst-year university students and seniors about their level of engagement in campus and classroom activities that enhance learning. Hundreds of thousands of
If you have an Instagram account, you are allowed to follow up to 7500 other accounts. At that point, Instagram cuts you off, and you have to “unfollow” people to add more.Imagine you collected data from Instagram users at your university about the number of accounts each one follows.a. What
A researcher collects data on the ages of university students. As you have probably observed, the distribution of age clusters around 19 to 22 years, but there are extremes on both the low end (high school prodigies) and the high end(nontraditional students returning to school).
Would the data for number of murders by those convicted of the crime be an example of a oor effect or a ceiling effect?
If the average person convicted of murder killed only one person, serial killers would create what kind of skew?
Referring to the histogram in Figure 2-1, how many countries had one or two volcanoes?
Referring to the grouped frequency table in Table 2-6, how many countries had at least 30 volcanoes?
A grouped frequency table has the following intervals: 30–44, 45–59, and 60–74. If converted into a histogram, what would the midpoints be?
If you have data that range from 2 to 68 and you want seven intervals in a grouped frequency table, what would the intervals be?
On a test of marital satisfaction, scores could range from 0 to 27.a. What is the full range of data, according to the calculation procedure described in this chapter?
Report the following numbers to two decimal places:0.0391, 198.2219, and 17.886.
Throughout this book, nal answers are reported to two decimal places. Report the following numbers this way:1888.999, 2.6454, and 0.0833.
Convert 2 out of 2000 into a percentage. Now convert 60 out of 62 into a percentage.
Counts are oen converted to percentages. Convert 817 out of 22,140 into a percentage. Now convert 4009 out of 22,140 into a percentage. What type of variable (nominal, ordinal, or scale)are these data as counts? What kind of variable are they as percentages?
Convert the following to percentages: 7 out of 39; 122 out of 300.
Convert the following to percentages: 63 out of 1264; 2 out of 88.
What is a ceiling effect and how does it affect a distribution?
What is a oor effect and how does it affect a distribution?
How do positively skewed distributions and negatively skewed distributions deviate from a normal distribution?
What is a normal distribution?
In your own words, dene the word distribution, rst as you would use it in everyday conversation and then as a statistician would use it.
What is the benet of creating a visual distribution of data rather than simply looking at a list of the data?
Describe what a histogram looks like, including what goes on the x-axis and the y-axis.
What are the typical labels for the x-axis and the y-axis in a histogram?
What is the difference between a histogram and a bar graph?
Describe two ways that statisticians might use the word interval.
What is the difference between a frequency table and a grouped frequency table?
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