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theory of statistics

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

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).They had
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 the data
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 on food
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 goodvertising.site/the-fun-theory.) For
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 per
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 gure skaters. They compared the gure
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, the
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, the
An independent-samples t test, award-winning television, and the theory of mind: Does watching awardwinning ction on television help us to understand other people? Psychologists Jessica Black and Jennifer Barnes (2015)tested whether people who watched award-winning ctional television shows like Mad
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 bulb
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 that
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 reect the actual means and the
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 in the
Making a decision: Numeric results for several independent-samples t tests are presented here. Decide whether each test is statistically signicant, 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 statistic
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 performing a
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
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.
71.30
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 4
How do we interpret effect size using Cohen’s d?
For an independent-samples t test, what is the difference between the formula for the t statistic and the formula for Cohen’s d?
Explain how we determine standard deviation (needed to calculate Cohen’sd) from the several steps of calculations we made to determine standard error.
Why does the effect-size calculation use standard deviation rather than standard error?
How does the size of the condence interval relate to the precision of the prediction?
What is the difference between pooled variance and pooled standard deviation?
How do condence intervals relate to margin of error?
Dene the symbols in the following formula:s 2difference = s 2MX + s 2MY
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?
What is pooled variance?
What is the difference between s 2X and s 2Y ?
As measures of variability, what is the difference between standard deviation and variance?
As they relate to comparison distributions, what is the difference between mean dierences and dierences between means?
Explain how the paired-samples t test helps us evaluate individual differences and the independent-samples t test helps us evaluate group differences.
What are independent events?
Explain random assignment and what it controls.
When is it appropriate to use an independent-samples t test?
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 conict that arises when we try to name the color of ink the words are
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
years on death row, respectively. (All were men, although Aileen Wuornos, the serial killer portrayed by Charlize Theron in the 2003 lm Monster, was among the three prisoners executed by the state of Florida in 2002; Wuornos spent 10.69 years on death row.)a. Using symbolic notation and formulas
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 entire
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
Email, stress, and a paired-samples t test: Researchers wondered if frequent checking of email increases stress (Kushlev &Dunn, 2015). They randomly assigned half of their participants to check email just three times a day for a week, and then in the second week, to check email as oen as they
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 which
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 al.,
pounds. The average ideal wedding weight reported by 227 women was 136.0 pounds. The data below represent the ctional weights of eight women on the day they bought their wedding dress and on the day they got married. Did women lose weight for their wedding day?Dress purchase Wedding day 163 158 144
Paired-samples t tests, condence 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 unhealthy
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 ll out an“Attitudes Toward Statistics” scale at the beginning of the term and at the end of the term.a.
Paired-samples t test and graduate admissions: Is it harder to get into graduate programs in psychology or in history? We randomly selected ve institutions from among all U.S. institutions with graduate programs. The rst number for each is the minimum grade-point average (GPA) for applicants to the
Paired-samples t tests, condence 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
Brain exercises and a paired-samples t test: PowerBrainRx, a Hong Kong–based for-prot 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 mathematics,
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 control
Cultural change and replication: Psychologist Patricia Greeneld (2017) points out that failures to replicate do not necessarily indicate that the initial ndings were wrong. She explains: “Data on the connection between social change and behavioral change point to a new role for ‘replication’:
Cheating and a single-sample t test: Participants in a study(Chou, 2015) aimed at understanding cheating behaviors were asked to ip 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 rafe for money. The catch?
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 that
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 during
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 statistic.)
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:
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% condence interval for a two-tailed test.c. Calculate the effect size using Cohen’s d.
Assume we know the following for a paired-samples t test:N = 13, Mdifference =−0.77, s = 1.42.a. Calculate the t statistic.b. Calculate a 95% condence interval.c. Calculate the effect size using Cohen’s d.
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% condence interval.c. Calculate the effect size.
Consider the following data:Score 1 Score 2 Score 1 Score 2 45 62 15 26 34 56 51 56 22 40 28 33 45 48a. Calculate the paired-samples t statistic.b. Calculate the 95% condence interval.c. Calculate the effect size for the mean difference.
The following are mood scores for 12 participants before and aer watching a funny video clip (lower values indicate better mood).Before Aer Before Aer 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 hypothesis
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 decision
Assume eight participants completed a mood scale before and aer 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 0.01.
Identify critical t values for each of the following tests:a. A one-tailed, paired-samples t test performed on beforeand-aer 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 performed
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
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 aer a 12-week marriage counseling program. Using an alpha
Using Cohen’s conventions, interpret the effect sizes that you calculated in:a. Exercise 9.30cb. Exercise 9.31c
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% condence interval.c. Calculate the effect size using Cohen’s d.
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% condence interval.c. Calculate the effect size using Cohen’s d.
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
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 0.01
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
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 sampleb. As
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 statistic,
We use formulas to describe calculations. Find the error in each of the following formulas. Explain why each is incorrect and provide a correction.a. sM =s√N − 1b. t =(M − μM)σM
If an effort to replicate a study fails, what are two things that the failure could indicate about the original study?
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?
Why is a condence interval more useful than a single-sample t test or a paired-samples t test?
If we calculate the condence 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?
If we calculate the condence interval around the sample mean difference used for a paired-samples t test, and it includes the value of 0, what can we conclude?
Why is the population mean almost always equal to 0 for the null hypothesis in the two-tailed, paired-samples t test?
How is a paired-samples t test different from a single-sample t test?
How is a paired-samples t test similar to a single-sample t test?
Explain the distinction between the terms independent samples and paired samples as they relate to t tests.
When do we use a paired-samples t test?
What do we mean when we say we have a distribution of mean differences?
What is the appropriate effect size for a single-sample t test?
Why is a condence interval more useful than a single-sample t test?
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.
Why do the t distributions merge with the z distribution as sample size increases?
How are the critical t values affected by sample size and degrees of freedom?
What does the phrase “free to vary,” referring to a number of scores in a given sample, mean for statisticians?
When is it appropriate to use a single-sample t test?
Dene the symbols in the formula for the t statistic:
Explain why the standard error for the distribution of sample means is smaller than the standard deviation of sample scores.
How is the calculation of standard error different for a t test than for a z test?
Why do we modify the formula for calculating standard deviation when using t tests (and divide by N − 1)?
When should we use a t distribution?
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 about the

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