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essentials of statistics

Questions and Answers of Essentials Of Statistics

14.31 Data are provided here with descriptive statistics, a correlation coefficient, and a regression equation: r = 0.52, Yˆ = 2.643 + 0.469(X).X Y 4.00 6.00 6.00 3.00 7.00 7.00 8.00 5.00 9.00 4.00
14.30 Data are provided here with descriptive statistics, a correlation coefficient, and a regression equation: r = 0.426, Yˆ = 219.974 + 186.595(X). X Y 0.13 200.00 0.27 98.00 0.49 543.00 0.57
14.29 Given the regression line Yˆ = 49 − 0.18(X), make predictions for each of the following:a. X =−31b. X = 65c. X = 14
14.28 Given the regression line Yˆ =−6 + 0.41(X), make predictions for each of the following:a. X = 25b. X = 50c. X = 75
14.27 Let’s assume we know that age is related to bone density, with a Pearson correlation coefficient of −0.19. (Notice that the correlation is negative, indicating that bone density tends to be
14.26 Using the following information, make a prediction for Y, given an X score of 8: Variable X: M = 12, SD = 3 Variable Y: M = 74, SD = 18 Pearson correlation of variables X and Y = 0.46a.
14.25 Using the following information, make a prediction for Y, given an X score of 2.9: Variable X: M = 1.9, SD = 0.6 Variable Y: M = 10, SD = 3.2 Pearson correlation of variables X and Y = 0.31a.
14.24 What are some of the ethical issues associated with using regression to predict individuals’ future behavior?
14.23 In what ways have regression tools been used to predict individuals’ future behavior?
14.22 What is the difference between the symbol for the effect size for simple linear regression and the symbol for the effect size for multiple regression?
14.21 Why is multiple regression often more useful than simple linear regression?
14.20 If you know the correlation coefficient, how can you determine the proportionate reduction in error?
14.19 What is an orthogonal variable?
14.18 What information does the proportionate reduction in error give us?
14.17 What are the basic steps to calculate the proportionate reduction in error?
14.16 When drawing error lines between data points and the regression line, why is it important that these lines be perfectly vertical?
14.15 What is SStotal?
14.14 Explain why the regression equation is a better source of predictions than the mean.
14.13 What is the connection between regression to the mean and the bell-shaped normal curve?
14.12 Why are explanations of the causes behind relations explored with regression limited in the same way they are with correlation?
14.11 What is the difference between a small standard error of the estimate and a large one?
14.10 How are the sign of the correlation coefficient and the sign of the slope related?
14.9 Why do we also call the regression line the line of best fit?
14.8 What does the slope tell us?
14.7 When is the intercept not meaningful or useful?
14.6 What are the three steps to calculate the intercept?
14.5 The equation for a line is Yˆ = a + b(X). Define the symbols a and b.
14.4 What does each of the symbols stand for in the formula for the regression equation: z Yˆ = (rXY )(zX)?
14.3 Is there any difference between Yˆ and a predicted score for Y? Explain your answer.
14.2 How does the regression line relate to the correlation of two variables?
14.1 What does regression add above and beyond what we learn from correlation?
13.55 High school athletic participation and correlation: Researchers examined longitudinal data to explore the long-term effects of high school athletic participation in the United States (Lutz et
13.54 Availability of food, amount eaten, and correlation: Did you know that sometimes you eat more just because the food is in front of you? Geier et al., (2006) studied how portion size affected
13.53 Health care spending, longevity, and correlation: The New York Times columnist Paul Krugman (2006) used the idea of correlation in a newspaper column when he asked, “Is being an American bad
13.52 Divorce rate, margarine consumption, and big data: Using data from the National Vital Statistics Reports and the U.S. Department of Agriculture, Tyler Vigen (2015) demonstrated a strong
13.51 Flu epidemics and correlation: In 2009, researchers at Google demonstrated that they could detect the spread of flu epidemics in the United States based on the correlation between a set of
13.50 Psychologists, housewives of New Jersey, and a spurious correlation: An online tool, Google Correlate (which shut down in 2019), reported a correlation in regional Google searches in the United
13.49 Swearing, vocabulary, and correlation: Psychology researchers set out to test the folk assumption that people swear a lot because their overall vocabulary is limited (Jay & Jay, 2015). They
13.48 Facebook likes and correlation: Be careful what you “like.” Researchers examined the relations between the number of Facebook “likes” a person has posted and the researchers’ ability
13.47 Correlation versus causation, iPhones, and millennials: One newspaper headline, noting that 18- to 34-year-olds were increasingly likely to move back home following the 2007 release of the
13.46 Correlation versus causation and hate crimes: Using municipalities (i.e., towns, cities) in Germany as participants, researchers found an association between the numbers of anti-refugee posts
13.45 Arts education, correlation, and causality: The Broadway musical Annie and the Entertainment Industry Foundation teamed up to promote arts education programs for underserved children. In an ad
13.44 Standardized tests, correlation, and causality: A New York Times editorial (“Public vs. Private Schools,” 2006) cited a finding by the U.S. Department of Education that standardized test
13.43 Driving a convertible, correlation, and causality: How safe are convertibles? USA Today (Healey, 2006) examined the pros and cons of convertible automobiles. The Insurance Institute for Highway
13.42 IQ-boosting water and illusory correlation: The trashy tabloid Weekly World News published an article—“Water from Mountain Falls Can Make You a Genius”—stating that drinking water from
13.41 Traffic, running late, and bias: A friend tells you that there is a correlation between how late she’s running and the amount of traffic. Whenever she’s going somewhere and she’s behind
13.40 Trauma, masculinity, and hypothesis testing for correlation: Using the data and your work in the previous exercise, perform the remaining five steps of hypothesis testing to explore the
13.39 Trauma, masculinity, and correlation: See the description of Holiday’s experiment in Exercise 13.37. We calculated the correlation coefficient for the relation between the perception of a
13.38 Trauma, femininity, and hypothesis testing for correlation: Using the data and your work in the previous exercise, perform the remaining five steps of hypothesis testing to explore the relation
13.37 Trauma, femininity, and correlation: Graduate student Angela Holiday (2007) conducted a study examining perceptions of combat veterans suffering from mental illness. Participants read a
13.36 Cats, mental health problems, and scatterplots: Consider the scenario in the previous exercise again. The two variables under consideration were (1) number of cats owned and (2) level of mental
13.35 Cats, mental health problems, and the direction of a correlation: You may be aware of the stereotype about the “crazy” person who owns a lot of cats. Have you wondered whether the
13.34 Direction of a correlation: For each of the following pairs of variables, would you expect a positive correlation or a negative correlation between the two variables? Explain your answer.a. How
13.33 Externalizing behavior, anxiety, and hypothesis testing for correlation: Using the data in the previous exercise, perform all six steps of hypothesis testing to explore the relation between
13.32 Externalizing behavior, anxiety, and correlation: As part of their study on the relation between rejection and depression in adolescents (Nolan et al., 2003), researchers collected data on
13.31 Exercise, number of friends, and correlation: Does the amount that people exercise correlate with the number of friends they have? The accompanying table contains data collected in some of our
13.30 Obesity, age at death, and correlation: In a newspaper column, Paul Krugman (2006) mentioned obesity (as measured by body mass index) as a possible correlate of age at death.a. Describe the
13.29 Debunking astrology with correlation: The New York Times reported that an officer of the International Society for Astrological Research, Anne Massey, stated that a certain phase of the planet
13.28 Awe and correlation in the news: The New York Times reported on a study that examined the link between positive emotions and health. First citing previous research connecting negative moods
13.27 Grip strength, mortality, and correlation: An international team of researchers studied the association between grip strength (using a tool that measures the strength of participants’ hands)
13.26 Quick thinking, smooth talking, and a correlation: Australian psychologist William von Hippel and his colleagues examined the premise that the ability to think quickly would be related to
13.25 Calculate the degrees of freedom and the critical values, or cutoffs, assuming a two-tailed test with an alpha level of 0.05, for each of the following designs:a. Data are collected to examine
13.24 Calculate the degrees of freedom and the critical values, or cutoffs, assuming a two-tailed test with an alpha level of 0.05, for each of the following designs:a. Forty students were recruited
13.23 Using the following data:X Y 40 60 45 55 20 30 75 25 15 20 35 40 65 30a. Create a scatterplot.b. Calculate deviation scores and products of the deviations for each individual, and then sum all
13.22 Using the following data:X Y 394 25 972 75 349 25 349 65 593 35 276 40 254 45 156 20 248 75a. Create a scatterplot.b. Calculate deviation scores and products of the deviations for each
13.21 Using the following data:X Y 0.13 645 0.27 486 0.49 435 0.57 689 0.84 137 0.64 167a. Create a scatterplot.b. Calculate deviation scores and products of the deviations for each individual, and
13.20 For each of the pairs of correlation coefficients provided, determine which one indicates a stronger relation between variables:a. −0.28 and −0.31b. 0.79 and 0.61c. 1.0 and −1.0d. −0.15
13.19 Use Cohen’s guidelines to describe the strength of the following correlation coefficients:a. −0.28b. 0.79c. 1.0d. −0.015
13.18 Decide which of the three correlation coefficient values below goes with each of the scatterplots presented in the previous exercise.a. 0.545b. 0.018c. −0.20
13.17 Determine whether the data in each of the graphs provided would result in a negative or positive correlation coefficient.
13.16 What is the relation between big data and spurious correlations?
13.15 What is the big data approach?
13.14 Describe the third assumption of hypothesis testing with correlation.
13.13 What are the three basic steps to calculate the Pearson correlation coefficient?
13.12 What are the null and research hypotheses for correlations?
13.11 What is meant by a spurious correlation, and why might it be a Type I error?
13.10 Why can we not infer causation from correlation?
13.9 Explain how the sum of the product of deviations determines the sign of the correlation.
13.8 How are deviation scores used in assessing the relation between variables?
13.7 Explain how the correlation coefficient can be used as a descriptive statistic or an inferential statistic.
13.6 When we have a straight-line relation between two variables, we use a Pearson correlation coefficient. What does this coefficient describe?
13.5 What magnitude of a correlation coefficient is large enough to be considered important, or worth talking about?
13.4 What is the difference between a positive correlation and a negative correlation?
13.3 Describe a perfect correlation, including its possible coefficients.
13.2 What is a linear relation?
13.1 What is a correlation coefficient?
12.49 Feedback and ANOVA: Stacey Finkelstein and Ayelet Fishbach (2012) examined the impact of feedback in the learning process. The following is an excerpt from their abstract: “This article
12.48 Skepticism, self-interest, and two-way ANOVA: A study on motivated skepticism examined whether participants were more likely to be skeptical when it served their self-interest (Ditto & Lopez,
12.47 Negotiation, an interaction, and a graph: German psychologist David Loschelder and his colleagues (2014) conducted an experiment on negotiations. They cited tennis player Andy Roddick’s
12.46 Gender, pizza, and an interaction: Researchers examined whether men and women eat different amounts of food in the company of same-sex dining partners versus opposite-sex dining partners
12.45 College students, anxiety, depression, and a MANOVA: Jason Nelson and Noel Gregg (2012) conducted a study of college students with disabilities. They reported that: “A 3 × 3 × 2 MANOVA was
12.44 Math performance and type of ANOVA: Imagine that a university professor is interested in the effects of a new instructional method on the math performance of first-year university students. All
12.43 Body weight, salary, and the need for covariates: A nutritional software program called DietPower offers encouragement to its users when they sign in each day. In one instance, the program
12.42 Exercise, well-being, and type of ANOVA: Cox and colleagues (2006) studied the effects of exercise on well-being. There were three independent variables: age (18–20 years old, 35–45 years
12.41 Helping, payment, and interactions: Expanding on the work of Heyman and Ariely (2004) as described in the previous exercise, let’s assume a higher level of payment was included and the
12.40 Helping, payment, and two-way between-groups ANOVA: Heyman and Ariely (2004) were interested in whether effort and willingness to help were affected by the form and amount of payment offered in
12.39 Age, online dating, and two-way between-groups ANOVA: The data below were from the same 25-year-old participants described in How It Works 12.1, but now the scores represent the oldest age that
12.38 Grade-point average, fraternities, sororities, and two-way between-groups ANOVA: A sample of students from our statistics classes reported their grade-point averages (GPAs), indicated their
12.37 The cross-race effect, main effects, and interactions: Hugenberg, Miller, and Claypool (2007) conducted a study to better understand the cross-race effect, in which people have a difficult time
12.36 Gender, negotiating a salary, and an interaction: Eleanor Barkhorn (2012) reported in The Atlantic about differences in women’s and men’s negotiating styles. She first explained that

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