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essentials of statistics

Essentials Of Statistics For The Behavioral Sciences 5th Edition Susan A. Nolan, Thomas Heinzen - Solutions

5.34 Convert the following percentages to proportions:a. 87.3%b. 14.2%c. 1%
5.33 Convert the following percentages to proportions:a. 62.7%b. 0.3%c. 4.2%
5.32 Convert the following proportions to percentages:a. 0.0173b. 0.8c. 0.3719
5.31 On a game show, 8 people have won the grand prize and a total of 266 people have competed. Estimate the probability of winning the grand prize.
5.30 What is the probability of hitting a target if, in the long run, 71 out of every 489 attempts actually hit the target?
5.29 Explain why, given the general tendency people have of perceiving illusory correlations, it is important to collect objective data.
5.28 Explain why, given the general tendency people have of exhibiting the confirmation bias, it is important to collect objective data.
5.27 You are running a study with five conditions, numbered 1 through 5. Using an online random numbers generator, assign the first seven participants who arrive at your lab to conditions, not worrying about equal assignment across conditions.
5.26 Randomly assign eight people to three conditions of a study, numbered 1, 2, and 3 using an online random numbers generator. (Note: Assign people to conditions without concern for having an equal number of people in each condition.)
5.25 Airport security makes random checks of passenger bags every day. If 1 in every 10 passengers is checked, use an online random numbers generator to determine the first 6 people to be checked—that is, which one of the first 10 people, which one of the second set of 10 people, and so on?
5.24 Forty-three tractor-trailers are parked for the night in a rest stop along a major highway. You assign each truck a number from 1 to 43. Use an online random numbers generator to select four trucks to weigh as they leave the rest stop in the morning.
5.23 What is the difference between a Type I error and a Type II error?
5.22 What are the two decisions or conclusions we can make about our hypotheses, based on the data?
5.21 What is the difference between a null hypothesis and a research hypothesis?
5.20 One step in hypothesis testing is to randomly assign some members of the sample to the control group and some to the experimental group. What is the difference between these two groups?
5.19 What are the ways the term independent is used by statisticians?
5.18 We distinguish between probabilities and proportions. How does each capture the likelihood of an outcome?
5.17 Statisticians use terms like trial, outcome, and success in a particular way in reference to probability. What do each of these three terms mean in the context of flipping a coin?
5.16 In your own words, what is expected relative-frequency probability?
5.15 In your own words, what is personal probability?
5.14 How does the confirmation bias lead to the perpetuation of an illusory correlation?
5.13 What is an illusory correlation?
5.12 What is the confirmation bias?
5.11 Ideally, an experiment would use random sampling so that the data would accurately reflect the larger population. For practical reasons, this is difficult to do. How does random assignment help make up for a lack of random sampling?
5.10 What does it mean to replicate research, and how does replication affect our confidence in the findings?
5.9 What is the difference between random sampling and random assignment?
5.8 What is a constraints on generality (COG) statement?
5.7 What does WEIRD stand for, and what is the problem that led to the coining of this term?
5.6 What are some of the pros and cons of crowdsourced data?
5.5 What is crowdsourcing in research?
5.4 What is a volunteer sample, and what is the main risk associated with it?
5.3 What is generalizability?
5.2 What is the difference between a random sample and a convenience sample?
5.1 Why do we study samples rather than populations?
4.48 Central tendency and outliers for data on traffic deaths: Below are estimated numbers of annual road traffic deaths for 12 countries based on data from the World Health Organization (apps.who.int/gho/data/view.main.51310):a. Compute the mean and the median across these 12 data points.b.
4.47 Descriptive statistics and basketball wins: Here are the numbers of wins for the 30 National Basketball Association teams in one season. 60 44 39 29 23 57 50 43 37 27 49 42 37 29 19 56 51 40 33 26 48 42 31 25 18 53 44 40 29 23a. Create a grouped frequency table for these data.b. Create a
4.46 Range, world records, and a long chain of friendship bracelets: Guinness World Records reported that, as part of an anti-bullying campaign, elementary school students in Pennsylvania created a chain of friendship bracelets that was a world-record 2678 feet long
4.45 Standard deviation and a texting intervention for parents of preschoolers: Researchers investigated READY4K, a program in which parents received text messages over an 8-month period (York & Loeb, 2014). The goal of the text messages was to help parents prepare their preschool-aged children for
4.44 Median ages and technology companies: In an article titled “Technology Workers Are Young (Really Young),” The New York Times reported median ages for a number of companies (Hardy, 2013). The reporter wrote: “The seven companies with the youngest workers, ranked from youngest to highest
4.43 Mean versus median for age at first marriage: The mean age at first marriage was 31.1 years for men and 29.1 years for women in Canada in 2008 (open.canada.ca/en/open-data). The median age at first marriage was 28.9 years for men and 26.9 years for women in the United States in 2011
4.42 Teaching assistants, race, and standard deviations: Researchers reported that the race of the teaching assistants (TAs) for a class had an effect on student outcome (Lusher et al., 2015). They reported that “Asian students receive a 2.3% of a standard deviation increase in course grade when
4.41 Central tendency and outliers from growth-chart data: When the average height or average weight of children is plotted to create growth charts, do you think it would be appropriate to use the mean for these data? There are often outliers for height, but why might we not have to be concerned
4.40 Outliers, H&M, and designer collaborations: The relatively low-cost Swedish fashion retailer H&M occasionally partners with high-end designers. For example, it collaborated with the Italian designer brand Moschino, and the line quickly sold out. If H&M were to report the average number of
4.39 Outliers, Hurricane Sandy, and a rat infestation: In a New York Times article, reporter Cara Buckley (2013) described the influx of rats inland from the New York City shoreline following the flooding caused by Hurricane Sandy. Buckley interviewed pest-control expert Timothy Wong, who noted
4.38 Shapes of distributions, chemistry grades, and first-generation college students: David Laude was a chemistry professor at the University of Texas at Austin (and a former underprepared college student) who developed an intervention that led underprepared students to perform at the same average
4.37 Central tendency and the shapes of distributions: Consider the many possible distributions of grades on a quiz in a statistics class; imagine that the grades could range from 0 to 100. For each of the following situations, give a hypothetical mean and median (i.e., make up a mean and a median
4.36 Statistics versus parameters: For each of the following situations, state whether the mean or median would be a statistic or a parameter. Explain your answer.a. According to Canadian census data, the median family income in British Columbia was $66,970, lower than the national median of
4.35 Descriptive statistics for data from the National Survey of Student Engagement: Every year, the National Survey of Student Engagement (NSSE) asks U.S. university students how many 20-page papers they had been assigned. Here are the percentages, for 1 year, of students who said they had been
4.34 Range of data for Canadian TV ratings: Numeris (formerly BBM Canada) collects Canadian television ratings data (en.numeris.ca). The following are the average number of viewers per minute (in thousands) for the top 30 English-language shows for 1 week. The NHL playoffs are listed at 1198, which
4.33 Descriptive statistics in the media: When there is an ad on TV for a body-shaping product (e.g., an abdominal muscle machine), often a person with a wonderful success story is featured in the ad. The statement “Individual results may vary” hints at what kind of data the advertisement may
4.32 Descriptive statistics in the media: Find an advertisement for an anti-aging product either online or in the print media—the more unbelievable the claims, the better!a. What does the ad promise that this product will do for the consumer?b. What data does it offer for its promised benefits?
4.31 Mean versus median in “real life”: Briefly describe a real-life situation in which the median is preferable to the mean. Give hypothetical numbers for the mean and median in your explanation. Be original! (Don’t use home prices or another example from the chapter.)
4.30 Measures of central tendency for measures of baseball performance: Here are winning percentages for 11 baseball players for their best 4-year pitching performances: 0.755 0.721 0.708 0.773 0.782 0.747 0.477 0.817 0.617 0.650 0.651a. What is the mean of these scores?b. What is the median of
4.29 Outliers, central tendency, and data on wind gusts: There appears to be an outlier in the data for peak wind gust recorded on top of Mount Washington (see the data in Exercise 4.19). Where do you see an outlier and how does excluding this data point affect the different calculations of central
4.28 Measures of central tendency for weather data: The “normal” weather data from the Mount Washington Observatory are broken down by month. Why might you not want to average across all months in a year? How else could you summarize the year?
4.27 Mean versus median for depression scores: A depression research unit recently assessed seven participants chosen at random from the university population. Is the mean or the median a better indicator of the central tendency of these seven participants? Explain your answer.
4.26 Mean versus median for temperature data: For the data in Exercise 4.19, the “normal” daily maximum and minimum temperatures recorded at the Mount Washington Observatory are presented for each month. These are likely to be measures of central tendency for each month over time. Explain why
4.25 Mean versus median for salary data: In Exercises 4.17 and 4.18, we saw how the mean and median changed when an outlier was included in the computations. If you were reporting the “average” salary at a company, how might the mean and the median give different impressions to potential
4.24 Here are recent U.S. News & World Report data on acceptance rates at the top 70 national universities. These are the percentages of accepted students out of all students who applied. 6.3 14.0 8.9 21.6 40.6 51.2 50.5 69.4 42.4 68.3 8.5 12.4 18.0 30.4 31.4 51.3 47.5 49.4 54.6 63.5 7.7 12.8 18.8
4.23 Why is the interquartile range you calculated for the previous exercise so much smaller than the range you calculated in Exercise 4.19?
4.22 Using the data presented in Exercise 4.19, calculate the interquartile range for peak wind gust.
4.21 Calculate the interquartile range for the following set of data: 2 5 1 3 3 4 3 6 7 1 4 3 7 2 2 2 8 3 3 12 1
4.20 Calculate the range and the interquartile range for the following set of data. Explain why they are so different.83 99 103 65 66 77 55 82 93 93 108 543 72 109 115 85 92 74 101 98 84
4.19 The Mount Washington Observatory (MWO) in New Hampshire claims to have the world’s worst weather. Below are some data on the weather extremes recorded at the MWO. Month Normal Daily Maximum (°F) Normal Daily Minimum (°F) Record Low in °F (year) Peak Wind Gust in Miles per Hour (year)
4.18 Use the following salary data for this exercise: $44,751 $38,862 $52,000 $51,380 $41,500 $61,774a. Calculate the mean, the median, and the mode.b. Add another salary, $97,582. Calculate the mean, median, and mode again. How does this new salary affect the calculations?c. Calculate the range,
4.17 Use the following data for this exercise: 15 34 32 46 22 36 34 28 52 28a. Calculate the mean, the median, and the mode.b. Add another data point, 112. Calculate the mean, median, and mode again. How does this new data point affect the calculations?c. Calculate the range, variance, and standard
4.16 Find the incorrectly used symbol or symbols in each of the following statements or formulas. For each statement or formula, (1) state which symbol(s) is/are used incorrectly, (2) explain why the symbol(s) in the original statement is/are incorrect, and (3) state which symbol(s) should be
4.15 Why is the standard deviation typically reported, rather than the variance?
4.14 Define the symbols used in the equation for variance: SD2 = Σ(X − M) 2 N
4.13 Explain the concept of standard deviation in your own words.
4.12 At what percentile is the third quartile?
4.11 At what percentile is the first quartile?
4.10 Using your knowledge of how to calculate the median, describe how to calculate the first and third quartiles of your data.
4.9 How does the interquartile range differ from the range?
4.8 In which situations is the mode typically used?
4.7 How do outliers affect the mean and the median?
4.6 What is an outlier?
4.5 Explain why the mean might not be useful for a bimodal or multimodal distribution.
4.4 Explain what is meant by unimodal, bimodal, and multimodal distributions.
4.3 Explain how the mean mathematically balances the distribution.
4.2 The mean can be assessed visually and arithmetically. Describe each method.
4.1 Define the three measures of central tendency: mean, median, and mode.
3.56 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
3.55 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.a. On what day and at what time is the highest average positive attitude expressed?b. On what day
3.54 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
3.53 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).
3.52 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
3.51 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.a. What is the primary flaw in the presentation of these data?b. How would you redesign this graph? Be specific and cite at least
3.50 Interpreting a graph about traffic flow: Go to maps.google.com. On a map of your country, select “Traffic” from the drop-down menu in the upper left corner.a. How is the density and flow of traffic represented in this graph?b. Describe traffic patterns in different regions of your
3.49 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 recently
3.48 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 field of psychology. The accompanying graph tracks the number of bachelor’s, master’s, and doctoral degrees
3.47 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) identified two
3.46 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.a. Briefly summarize the main point of the article and graph.b. What are the independent and dependent variables depicted in the graph? What kinds of
3.45 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 specific—don’t just say that there is
3.44 Software 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 ordinary behaviors are given game-like incentives to promote prosocial behaviors such as recycling or
3.43 Software 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
3.42 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
3.41 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
3.40 Survey of Earned Doctorates and a dot plot: Use the data from Exercise 2.30 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.b. What can you learn about the shape of this distribution from this dot plot?
3.38 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 specifically, we created a Pareto chart.a. Explain the difference between a Pareto chart and a

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