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essentials of statistics

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

10.40 Gender and number words: Chang, Sandhofer, and Brown (2011) wondered whether mothers used number words more, on average, with their preschool sons than with their preschool daughters. Each participating family included one mother and one child—either female or male. The researchers
10.39 Gender, humor, and reporting statistical results in APA style: How would we report the results of the hypothesis test and the effect size calculation for the gender and humor data that you conducted in Exercises 10.36 and 10.38?
10.38 Gender, humor, and effect size for an independentsamples t test: How can we calculate an effect size for the independent-samples t test we conducted in Exercise 10.36?
10.37 Gender, humor, and a confidence interval for an independent-samples t test: Calculate a 95% confidence interval for the independent-samples t test you conducted on the gender and humor data in the previous exercise.
10.36 Gender, humor, and an independent-samples t test: Researchers at Stanford University examined brain activity in women and men during exposure to humorous cartoons (Azim et al., 2005). Using functional magnetic resonance imaging (fMRI), researchers observed more activity in the reward centers
10.35 Independent-sample t tests and note-taking—laptop or longhand: Researchers explored whether there were mean differences between students who were randomly assigned to take notes longhand and students who were randomly assigned to take notes on their laptops (Mueller & Oppenheimer, 2014).
10.34 Independent-sample t tests and “Blinded with Science”: Researchers studied the effects of learning about the effectiveness of a new medication (Tal & Wansink, 2016). Some participants heard information about the medication; others heard the same information and saw a graph that depicted
10.33 Cafeteria trays, food consumption, and an independentsamples t test: Kiho Kim and Stevia Morawski (2012) reported the following in the abstract (brief summary) of their published research study: “Here, we report on the results of an experiment to evaluate the effects of tray availability
10.32 Independent-sample t tests and the “fun theory”: Volkswagen has created a series of videos based on its “fun theory, ” the idea that you can change behavior if you take an activity that is good for society and make it fun. (You can watch the videos at
10.31 Independent-samples t test and walking speed: The New York City Department of City Planning (2006) studied pedestrian walking speeds. The report stated that pedestrians who were en route to work walked a median of 4.41 feet per second, whereas tourist pedestrians walked a median of 3.79 feet
10.30 Null and research hypotheses: Using the research studies described in the previous exercise, create null hypotheses and research hypotheses appropriate for the chosen statistical test:a. Taylor and Ste-Marie (2001) studied eating disorders in 41 Canadian female figure skaters. They compared
10.29 Choosing a hypothesis test: For each of the following three scenarios, state which hypothesis test you would use from among the four introduced so far: the z test, the single-sample t test, the paired-samples t test, and the independent-samples t test. (Note: In the actual studies described,
10.28 Choosing a hypothesis test: For each of the following three scenarios, state which hypothesis test you would use from among the four introduced so far: the z test, the single-sample t test, the paired-samples t test, and the independent-samples t test. (Note: In the actual studies described,
10.27 An independent-samples t test, award-winning television, and the theory of mind: Does watching awardwinning fiction on television help us to understand other people? Psychologists Jessica Black and Jennifer Barnes (2015) tested whether people who watched award-winning fictional television
10.26 An independent-samples t test and getting people to turn off the light: Do you turn off the light when you leave the room? South Korean researchers wondered how they could increase the number of people who do (Ahn et al., 2014). They compared two poster campaigns. In one, an image of a light
10.25 An independent-samples t test, gender, and talkativeness: “Are Women Really More Talkative Than Men?” is the title of an article that appeared in the journal Science. In the article, Mehl et al. (2007) report the results of a study of 396 men and women. Each participant wore a microphone
10.24 An independent-samples t test and getting ready for a date: In an example, we sometimes use in our statistics classes, several semesters’ worth of male and female students were asked how long, in minutes, they spend getting ready for a date. The data reported below reflect the actual means
10.23 The independent-samples t test, hypnosis, and the Stroop effect: Using data from Exercise 9.61 on the effects of posthypnotic suggestion on the Stroop effect (Raz et al., 2005), let’s conduct an independent-samples t test. For this test, we will pretend that two sets of people participated
10.22 Making a decision: Numeric results for several independent-samples t tests are presented here. Decide whether each test is statistically significant, and report each result in the standard APA format.a. A total of 73 people were studied, 40 in one group and 33 in the other group. The test
10.21 Find the critical t values for the following data sets:a. Group 1 has 21 participants and Group 2 has 16 participants. You are performing a two-tailed test with an alpha of 0.05.b. You studied 3-year-old children and 6-year-old children, with samples of 12 and 16, respectively. You are
10.20 Consider the following data from two independent groups: Liberals: 2, 1, 3, 2 Conservatives: 4, 3, 3, 5, 2, 4a. Calculate s 2 for each group.b. Calculate dfX, dfY , and dftotal.c. Determine the critical values for t, assuming a two-tailed test with an alpha level of 0.05.d. Calculate pooled
10.19 Consider the following data from two independent groups: Group 1: 97, 83, 105, 102, 92 Group 2: 111, 103, 96, 106a. Calculate s 2 for Group 1 and for Group 2.b. Calculate dfX, dfY , and dftotal.c. Determine the critical values for t, assuming a two-tailed test with an alpha level of 0.05.d.
10.18 In the next column are several sample means. For each class, calculate the differences between the means for students who sit in the front versus the back of a classroom. Mean test grades Students in the front Students in the back Class 1 82.0 78.00 Class 2 79.5 77.41 Class 3 71.5 76.00 Class
10.17 How do we interpret effect size using Cohen’s d?
10.16 For an independent-samples t test, what is the difference between the formula for the t statistic and the formula for Cohen’s d?
10.15 Explain how we determine standard deviation (needed to calculate Cohen’sd) from the several steps of calculations we made to determine standard error.
10.14 Why does the effect-size calculation use standard deviation rather than standard error?
10.13 How does the size of the confidence interval relate to the precision of the prediction?
10.12 What is the difference between pooled variance and pooled standard deviation?
10.11 How do confidence intervals relate to margin of error?
10.10 Define the symbols in the following formula: s 2 difference = s 2 MX + s 2 MY
10.9 Why would we want the variability estimate based on a larger sample to count more (to be more heavily weighted) than one based on a smaller sample?
10.8 What is pooled variance?
10.7 What is the difference between 8 and s?
10.6 As measures of variability, what is the difference between standard deviation and variance?
10.5 As they relate to comparison distributions, what is the difference between mean differences and differences between means?
10.4 Explain how the paired-samples t test helps us evaluate individual differences and the independent-samples t test helps us evaluate group differences.
10.3 What are independent events?
10.2 Explain random assignment and what it controls.
10.1 When is it appropriate to use an independent-samples t test?
9.61 Hypnosis and the Stroop effect: In Chapter 1, you were given an opportunity to complete the Stroop test, in which color words are printed in the wrong color; for example, the word red might be printed in the color blue. The conflict that arises when we try to name the color of ink the words
9.60 Political bias in academia and a paired-samples t test: The following is an excerpt from the abstract (brief opening summary) from a published research study that examined a reported bias against conservatives in American academia (Fosse et al., 2011). The American professoriate contains a
9.59 Death row and the single-sample t test: The Florida Department of Corrections publishes an online death row fact sheet. It reports the average time on death row prior to execution as 11.72 years but provides no standard deviation. This mean is a parameter because it is calculated from the
9.58 Paid days off and the single-sample t test: The number of paid days off (e.g., vacation, sick leave) taken by eight employees at a small local business is compared to the national average. You are hired as a consultant by the new business owner to help her determine how many paid days off she
9.56 A paired-samples t test and English-language tests for international students: The International English Language Testing System (IELTS) is a test that assesses the English-language skills of international students who wish to study in an Englishspeaking country. It has six modules, one of
9.55 Paired-samples t test, decorations in kindergarten classrooms, and science learning: Psychology researcher Anna Fisher and her colleagues studied whether kindergarten students learned better in decorated classrooms or undecorated classrooms, referred to as “sparse classrooms” (Fisher et
9.54 Paired-samples t tests, confidence intervals, and weddingday weight loss: It seems that 14% of engaged women buy a wedding dress at least one size smaller than their current size. Why? Cornell researchers reported an alarming tendency for women who are engaged to sometimes attempt to lose an
9.53 Attitudes toward statistics and the paired-samples t test: A professor wanted to know if her students’ attitudes toward statistics changed by the end of the course, so she asked them to fill out an “Attitudes Toward Statistics” scale at the beginning of the term and at the end of the
9.52 Paired-samples t test and graduate admissions: Is it harder to get into graduate programs in psychology or in history? We randomly selected five institutions from among all U.S. institutions with graduate programs. The first number for each is the minimum grade-point average (GPA) for
9.51 Paired-samples t tests, confidence intervals, and hockey goals: Below are the numbers of goals scored by the leading scorers on the New Jersey Devils ice hockey team in the 2007–2008 and 2008–2009 seasons. On average, did the Devils play any differently in 2008–2009 than they did in
9.50 Brain exercises and a paired-samples t test: PowerBrainRx, a Hong Kong–based for-profit company, promises to improve cognition. Its Web site lists testimonials, including one from a parent whose children “seemed to have better working memories, improved problem-solving ability like
9.49 A single-sample t test and Victoria’s Secret perfume as an insect repellent: Biology researchers examined the mosquitorepelling effects of a control (no scent), insect repellents that contain DEET, natural insect repellents, and several beauty products (Rodriguez et al., 2015). In the
9.48 Cultural change and replication: Psychologist Patricia Greenfield (2017) points out that failures to replicate do not necessarily indicate that the initial findings were wrong. She explains: “Data on the connection between social change and behavioral change point to a new role for
9.47 Cheating and a single-sample t test: Participants in a study (Chou, 2015) aimed at understanding cheating behaviors were asked to flip a coin 20 times and report—on the honor system—how many heads they received. The more heads, the more entries they would receive for a raffle for money.
9.46 t tests and the cost of Levi’s jeans and H&M dresses in Halifax: Numbeo is a crowdsourced Web site that gathers data on cities and countries around the world (numbeo.com/cost-of-living). The data are searchable by city or country. For example, when we looked up Halifax, Canada, we discovered
9.45 Single-sample t test, military training, and anger: Bardwell, Ensign, and Mills (2005) assessed the moods of 60 male U.S.Marines following a month-long training exercise conducted in cold temperatures and at high altitudes. Negative moods, including fatigue and anger, increased substantially
9.44 t statistics and standardized tests: On its Web site, the Princeton Review claims that students who have taken its course improve their Graduate Record Examination (GRE) scores, on average, by 210 points (based on the old scoring system). (No other information is provided about this
9.43 The relation between the z distribution and the t distributions: For the hypothesis tests described in parts (a) through (c), identify what the critical z value would have been if there had been just one sample and we knew the mean and standard deviation of the population:a. A single-sample t
9.42 Assume we know the following for a paired-samples t test: N = 32, Mdifference = 1.75, s = 4.0.a. Calculate the t statistic.b. Calculate a 95% confidence interval for a two-tailed test.c. Calculate the effect size using Cohen’sd. Applying the Concepts
9.40 Consider the following data.Score 1 Score 2 23 16 30 12 28 25 30 27 14 6a. Calculate the paired-samples t statistic.b. Calculate the 95% confidence interval.c. Calculate the effect size. 9.41 Assume we know the following for a paired-samples t test: N = 13, Mdifference =−0.77, s = 1.42.a.
9.38 The following are mood scores for 12 participants before and after watching a funny video clip (lower values indicate better mood).Before After Before After 7 2 4 2 5 4 7 3 5 3 4 1 7 5 4 1 6 5 5 3 7 4 4 3a. Calculate the paired-samples t statistic for these mood scores.b. Using a one-tailed
9.37 The following are scores for eight students on two different exams. Exam 1 Exam 2 92 84 67 75 95 97 82 87 73 68 59 63 90 88 72 78a. Calculate the paired-samples t statistic for these exam scores.b. Using a two-tailed test and an alpha level of 0.05, identify the critical t values and make a
9.36 Assume eight participants completed a mood scale before and after watching a funny video clip.a. Identify the critical t value for a one-tailed, paired-samples t test with an alpha level of 0.01.b. Identify the critical t values for a two-tailed, paired-samples t test with an alpha level of
9.35 Identify critical t values for each of the following tests:a. A one-tailed, paired-samples t test performed on beforeand-after scores on the Marital Satisfaction Inventory for 18 people who went through marriage counseling, using an alpha level of 0.01.b. A two-tailed, paired-samples t test
9.34 Market researchers collected information on smartphone data usage for Uber drivers. They wondered if Uber drivers use a higher amount of smartphone data compared to all other taxi drivers. A total of 31 Uber drivers reported their monthly data usage. Using an alpha level of 0.10, identify the
9.33 Identify the critical t values for each of the following tests:a. Researchers wanted to know if marriage counseling improved participants’ marital satisfaction. Scores were collected on the Marital Satisfaction Inventory for 15 people after a 12-week marriage counseling program. Using an
9.32 Using Cohen’s conventions, interpret the effect sizes that you calculated in:a. Exercise 9.30cb. Exercise 9.31c
9.31 Assume we know the following for a two-tailed, single-sample t test: μ = 7, N = 41, M = 8.5, s = 2.1.a. Calculate the t statistic.b. Calculate a 99% confidence interval.c. Calculate the effect size using Cohen’s d.
9.30 Assume we know the following for a two-tailed, single-sample t test, at an alpha level of 0.05: μ = 44.3, N = 114, M = 43, s = 5.9.a. Calculate the t statistic.b. Calculate a 95% confidence interval.c. Calculate the effect size using Cohen’s d.
9.29 Identify the critical t values for each of the following tests:a. A single-sample t test examining scores for 26 participants to see if there is any difference compared to the population, using an alpha level of 0.05b. A one-tailed, single-sample t test performed on scores on the Marital
0.01
9.28 Calculate degrees of freedom and identify the critical t value for a single-sample t test in each of the following circumstances:a. Two-tailed test, N = 8, alpha level of 0.10b. One-tailed test, N = 42, alpha level of 0.05c. Two-tailed test, N = 89, alpha level of
9.27 Identify the critical t value in each of the following circumstances:a. One-tailed test, df = 73, alpha level of 0.10b. Two-tailed test, df = 108, alpha level of 0.05c. One-tailed test, df = 38, alpha level of 0.01
9.26 For the data 1.01, 0.99, 1.12, 1.27, 0.82, 1.04, calculate the standard deviation under the conditions in parts (a) and (b). Then, complete parts (c) and (d). (Note: You will have to carry some calculations out to the third decimal place to see the difference in calculations.)a. For the
9.25 For the data 93, 97, 91, 88, 103, 94, 97, calculate the standard deviation under the conditions in parts (a) and (b). Then, complete parts (c) and (d).a. For this sampleb. As an estimate of the populationc. Calculate the standard error for t using symbolic notation.d. Calculate the t
9.24 We use formulas to describe calculations. Find the error in each of the following formulas. Explain why each is incorrect and provide a correction.
9.23 If an effort to replicate a study fails, what are two things that the failure could indicate about the original study?
9.22 What is the appropriate effect size for a paired-samples t test? How is the calculation different from the effect size for a singlesample t test?
9.21 Why is a confidence interval more useful than a single-sample t test or a paired-samples t test?
9.20 If we calculate the confidence interval around the sample mean difference used for a paired-samples t test, and it does not include the value of 0, what can we conclude?
9.19 If we calculate the confidence interval around the sample mean difference used for a paired-samples t test, and it includes the value of 0, what can we conclude?
9.18 Why is the population mean almost always equal to 0 for the null hypothesis in the two-tailed, paired-samples t test?
9.17 How is a paired-samples t test different from a single-sample t test?
9.16 How is a paired-samples t test similar to a single-sample t test?
9.14 When do we use a paired-samples t test? 9.15 Explain the distinction between the terms independent samples and paired samples as they relate to t tests.
9.13 What do we mean when we say we have a distribution of mean differences?
9.11 Why is a confidence interval more useful than a single-sample t test? 9.12 What is the appropriate effect size for a single-sample t test?
9.10 Explain what each part of the following statistical phrase means, as it would be reported in APA format: t(4) = 2.87, p = 0.032.
9.9 Why do the t distributions merge with the z distribution as sample size increases?
9.8 How are the critical t values affected by sample size and degrees of freedom?
9.7 What does the phrase “free to vary, ” referring to a number of scores in a given sample, mean for statisticians?
9.6 When is it appropriate to use a single-sample t test?
9.5 Define the symbols in the formula for the t statistic:
9.4 Explain why the standard error for the distribution of sample means is smaller than the standard deviation of sample scores.
9.3 How is the calculation of standard error different for a t test than for a z test?
9.2 Why do we modify the formula for calculating standard deviation when using t tests (and divide by N − 1)?
9.1 When should we use a t distribution?
8.65 Effect size and an intervention to increase college applications: Caroline Hoxby and Sarah Turner (2013) conducted an experiment to determine whether a simple intervention could increase the number of college applications among low-income students. The intervention consisted of information
8.64 Sample size, effect size, and ESP: Bem (2011) reports nine experiments in which he presents evidence for extrasensory perception (ESP). For example, in Experiment 1, participants were shown two “curtains” side by side on a computer screen and told that there was a picture behind one
8.63 Fantasy baseball: Your roommate is reading Fantasyland: A Season on Baseball’s Lunatic Fringe (Walker, 2006) and is intrigued by the statistical methods used by competitors in fantasy baseball leagues (in which competitors select a team of baseball players from across all major league teams,

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