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theory of statistics

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

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 curtain and
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,
Meta-analysis and an examination of whether sex and violence sell: Researchers from The Ohio State University conducted a meta-analysis of 53 studies totaling almost 8500 participants (Lull & Bushman, 2015). Their goal was to determine whether advertising that included sex or violence helped to
Meta-analysis and math performance: Following is an excerpt of an abstract from a published meta-analysis by Lindberg and colleagues (2010). Use this excerpt to describe what is done in each of the four steps of meta-analysis.In this article, we use meta-analysis to analyze gender dierences in
Meta-analysis, mental health treatments, and cultural contexts (continued): The research paper on culturally targeted therapy described in the previous exercise reported the following:Across all 76 studies, the random eects weighted average eect size was d = .45(SE = .04, p < .0001), with a 95%
Meta-analysis, mental health treatments, and cultural contexts: A meta-analysis examined studies that compared two types of mental health treatments for ethnic and racial minorities—the standard available treatments and treatments that were adapted to the clients’ cultures (Griner & Smith,
Effect size and homeless families: A New York Times article reported on the growing problem of homelessness among families (Bellafante, 2013). The reporter wrote that families in a city-run program called Homebase had shorter stays than families not in the program—a difference of about 22.6 fewer
Type I errors, Type II errors, and ego depletion: Ego depletion refers to the idea that we have a limited amount of self-control, which can be depleted. Exerting self-control in one situation will make it harder to exert self-control on later tasks.For example, maybe you’re eating a healthy diet
Power analysis and enhancing memory: In a study of the effects of testing on enhancing memory, Akan and colleagues(2018) performed an a priori power analysis to determine the sample size they would need to detect a small- to medium-sized effect (d = 0.40) with 80% power and an alpha level of 0.05.
Condence intervals, effect sizes, and tennis serves(continued): As in the previous exercise, assume the average speed of a serve in women’s tennis is around 118 mph, with a standard deviation of 12 mph. But now we recruit only 26 amateur tennis players to use our method. Again, aer 6 months we
More about condence intervals, effect sizes, and tennis serves: Let’s assume the average speed of a serve in women’s tennis is around 118 mph, with a standard deviation of 12 mph.We recruit 100 amateur tennis players to use our new training method this time, and aer 6 months we calculate a
Condence intervals, effect sizes, and Valentine’s Day spending: According to the Nielsen Company, Americans spend$345 million on chocolate during the week of Valentine’s Day.Let’s assume that we know the average married person spends$45, with a population standard deviation of $16. In
Effect size and English-language tests for international students (continued): In the previous exercise, you calculated an effect size for data for 63 international students at the University of Melbourne. Imagine that you had a sample of 300 students. How would the effect size change? Explain why
Effect size and English-language tests for international students: In the two previous exercises, we considered the IELTS listening module, for which the population of all IELTS takers in a year had a mean score of 6.00 with a standard deviation of 1.30 (2013). A sample of 63 international students
Condence intervals and English-language tests for international students (continued): Using the IELTS listening data presented in the previous exercise, practice evaluating data using condence intervals.a. Compute the 80% condence interval.b. How do the conclusion and the condence interval change
Condence intervals and English-language tests for international students: The International English Language Testing System (IELTS) has six modules, one of which assesses listening skills. IELTS researchers reported that a recent mean for everyone who completed this module in 1 year was 6.00 and
Condence intervals, effect sizes, and tennis serves: Let’s assume the average speed of a serve in men’s tennis is around 135 mph, with a standard deviation of 6.5 mph. Because these statistics are calculated over many years and many players, we will treat them as population parameters. We
Overlapping distributions and English-language tests for international students: International students who wish to study at English-speaking universities in Canada or the United States are required to take a test, such as the Test of English as a Foreign Language (TOEFL) or the International
What does failing to reject the null mean?: If a researcher fails to reject the null hypothesis, how would knowing information about the sample size and the expected effect size help to interpret the researcher’s failure to reject the null hypothesis?
Sample size, z statistics, and the Graded Naming Test: In an exercise in Chapter 7, we asked you to conduct a z test to ascertain whether the Graded Naming Test (GNT) scores for Canadian participants differed from the GNT norms based on adults in England. We also used these data in the How It Works
and the population standard deviation (σ) is 0.70. Imagine that a sample of students had a mean of 3.45.a. Calculate the test statistic for a sample of ve students.b. Calculate the test statistic for a sample of 1000 students.c. Calculate the test statistic for a sample of 1,000,000 students.d.
Sample size, z statistics, and the Consideration of Future Consequences scale: Here are summary data from a z test regarding scores on the Consideration of Future Consequences scale (Petrocelli, 2003): The population mean (μ) is
Distributions and the Burakumin: A friend reads in her Introduction to Psychology textbook about a minority group in Japan, the Burakumin, who are racially the same as other Japanese people, but are viewed as outcasts because their ancestors were employed in positions that involved the handling of
Margin of error and adult education: According to a 2013 report by Public Agenda and the Kresge Foundation, online education is popular among adults planning to return to university. “The majority (73%) of adult prospective students want to take at least some classes online, and nearly 4 in
Assume you are conducting a meta-analysis over a set of ve studies. The effect sizes for each study follow:d = 1.23; d = 1.08; d =−0.35; d = 0.88; d = 1.69.a. Calculate the mean effect size for these studies.b. Use Cohen’s conventions to describe the mean effect size you calculated in part (a).
Assume you are conducting a meta-analysis over a set of 5 studies. The effect sizes for each study follow:d = 0.67; d = 0.03; d = 0.32; d = 0.59; d = 0.22.a. Calculate the mean effect size for these studies.b. Use Cohen’s conventions to describe the mean effect size you calculated in part (a).
A meta-analysis reports an average effect size of d = 0.11, with a condence interval of d =−0.06 to d = 0.28. Would a hypothesis test (assessing the null hypothesis that the average effect size is 0) lead us to reject the null hypothesis? Explain.
A meta-analysis reports an average effect size of d = 0.11, with a condence interval of d = 0.08 to d = 0.14.a. Would a hypothesis test (assessing the null hypothesis that the average effect size is 0) lead us to reject the null hypothesis? Explain.b. Use Cohen’s conventions to describe the
For each of the following z statistics, calculate the p value for a two-tailed test.a. 2.23b. −1.82c. 0.33
For each of the following d values, identify the size of the effect using Cohen’s guidelines.a. d = 1.22b. d =−1.22c. d = 0.13d. d =−0.13
For each of the following d values, identify the size of the effect using Cohen’s guidelines.a. d = 0.79b. d =−0.43c. d = 0.22d. d =−0.04
For each of the effect-size calculations in the previous exercise, identify the size of the effect using Cohen’s guidelines.Remember, for the SAT math exam, μ = 500 and σ = 100.a. Sixty-one people sampled have a mean of 480.b. Eighty-two people sampled have a mean of 520.c. Six people sampled
Calculate the effect size for each of the following average SAT math scores. Remember, the SAT math exam is standardized such that μ = 500 and σ = 100.a. Sixty-one people sampled have a mean of 480.b. Eighty-two people sampled have a mean of 520.c. Six people sampled have a mean of 610.
Calculate the effect size for the mean of 1057 observed in the previous exercise, where μ = 1014 and σ = 136.
For a given variable, imagine we know that the population mean is 1014 and the standard deviation is 136. A sample mean of 1057 is obtained. Calculate the z statistic for this mean, using each of the following sample sizes:a. 12b. 39c. 188
Calculate the standard error for each of the following sample sizes when μ = 1014 and σ = 136:a. 12b. 39c. 188
Calculate the 80% condence interval for the same ctional data regarding daily TV viewing habits:μ =
hours; σ =
Calculate the 95% condence interval for the following ctional data regarding daily TV viewing habits:μ =
For each of the following condence levels, look up the critical z values for a two-tailed z test.a. 80%b. 85%c. 99%
For each of the following condence levels, look up the critical z value for a one-tailed z test.a. 80%b. 85%c. 99%
For each of the following condence levels, indicate how much of the distribution would be placed in the cutoff region for a two-tailed z test.a. 80%b. 85%c. 99%
For each of the following condence levels, indicate how much of the distribution would be placed in the cutoff region for a one-tailed z test.a. 80%b. 85%c. 99%
percentage points” (p. 6).Fourteen percent of respondents indicated that they strongly agreed that massive open online courses (MOOCs) could have a positive impact on higher education. Construct an interval estimate for the point estimate of 14%.
In 2013, the Gallup polling organization and the online publication Inside Higher Ed reported the results of a survey of 831 university presidents and chancellors. The report stated:“For results based on the sample size of 831 total respondents, one can say with 95 percent condence that the
In 2008, 22% of Gallup respondents indicated that they were suspicious of steroid use by athletes who broke world records in swimming. Calculate an interval estimate using a margin of error at 3.5%.
In 2008, a Gallup poll asked people whether they were suspicious of steroid use among Olympic athletes. Thirty-ve percent of respondents indicated that they were suspicious when they saw an athlete break a track-and-eld record, with a 4% margin of error. Calculate an interval estimate.
What is the best way to avoid the negative consequences of an underpowered study?
What are the potential negative consequences of an underpowered study?
In statistics, concepts are oen expressed in symbols and equations. For d =(M − μ)σM, (i) identify the incorrect symbol,(ii) state what the correct symbol is, and (iii) explain why the initial symbol was incorrect.
Why is it important for a researcher who is conducting a meta-analysis to nd not only published studies but also unpublished studies?
What is the goal of a meta-analysis?
What are the four basic steps of a meta-analysis?
Traditionally, what minimum percentage chance of correctly rejecting the null hypothesis is suggested to proceed with an experiment?
How are statistical power and effect size different but related?
In your own words, dene the word power—rst as you would use it in everyday conversation and then as a statistician would use it.
How does statistical power relate to Type II errors?
What are Cohen’s guidelines for small, medium, and large effects?
What does it mean to say an effect-size statistic neutralizes the inuence of sample size?
Relate effect size to the concept of overlap between distributions.
What effect does increasing the sample size have on standard error and the test statistic?
In your own words, dene the word eect—rst as you would use it in everyday conversation and then as a statistician would use it.
What are the ve steps to create a condence interval for the mean of a z distribution?
Why do we calculate condence intervals?
In your own words, dene the word condence—rst as you would use it in everyday conversation and then as a statistician would use it in the context of a condence interval.
What specic danger exists when reporting a statistically signicant difference between two means?
Radiation levels on Japanese farms: Fackler (2012)reported in The New York Times that Japanese farmers have become skeptical of the Japanese government’s assurances that radiation levels were within legal limits in the wake of the 2011 tsunami and radiation disaster at Fukushima. Aer reports of
The Graded Naming Test and sociocultural differences:Researchers oen use z tests to compare their samples to known population norms. The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black-and-white drawings. The test, oen used to detect brain damage, starts with easy
Patient adherence and orthodontics: A research report(Behenam & Pooya, 2006) begins,“There is probably no other area of health care that requires … cooperation to the extent that orthodontics does,” and explores factors that affected the number of hours per day that Iranian patients wore
Power posing, p-hacking, and mixed results: In 2010, a group of researchers published the nding that power posing—adopting a wide stance with one’s hands on one’s hips—improved self-reported feelings of power and increased testosterone levels in a sample of 42 participants (Carney et al.,
Same data set, different answers, and p-hacking: Brian Nosek and other researchers at the Center for Open Science gave the exact same set of data on football players (soccer players in the United States and Canada) to 29 different teams of researchers (Silberzahn et al., 2018). The researchers were
HARKing and medical research: Imagine that an international team of medical researchers hypothesized that a new drug might cure a life-threatening disease. They test their hypothesis by recruiting 50 participants; half receive the drug, while the other half serve as a control group. At the end of
Passwords, redheads, and a z test: The BBC reported that red-haired women were more likely than others to choose strong passwords (Ward, 2013). How might a researcher study this? Computer scientist Cynthia Kuo and her colleagues (2006)conducted a study in which they gave passwords a score, with
Steps 1 and 2 of hypothesis testing for a study of the Wechsler Adult Intelligence Scale—Revised: Boone (1992)examined scores on the Wechsler Adult Intelligence Scale—Revised (WAIS-R) for 150 adult psychiatric inpatients. He determined the “intrasubtest scatter” score for each
The z distribution and Hurricane Katrina: Hurricane Katrina hit New Orleans on August 29, 2005. The National Weather Service Forecast Ofce maintains online archives of climate data for all U.S. cities and areas. These archives allow us to nd out, for example, how the rainfall in New Orleans that
Null hypotheses and research hypotheses: For each of the following examples, state the null hypothesis and the research hypothesis, in both words and symbolic notation:a. Musician David Teie worked with animal researchers to develop music specically for cats—music that a typical cat might nd
Directional versus nondirectional hypotheses: For each of the following examples, identify whether the research has expressed a directional or a nondirectional hypothesis:a. Musician David Teie worked with animal researchers to develop music specically for cats—music that a typical cat might nd
inches occur in this population?e. How does this result compare to the statistical signicance cutoff of 5%?
The z statistic, distributions of means, and heights of boys: Another teacher decides to average the heights of all 15-year-old male students in his classes throughout the day. By the end of the day, he has measured the heights of 57 boys and calculated an average of
inches.a. Calculate the mean and the standard error of the distribution of mean heights.b. Calculate the z statistic for this group.c. What percentage of mean heights, based on a sample size of 14 students, would we expect to be shorter than this group?d. How oen do mean heights equal to or more
inches [162.05 centimeters] and σ = 2.66 inches), imagine that a teacher nds the average height of 14 female students in one of her classes to be
The z statistic, distributions of means, and heights of girls: Using what we know about the height of 15-year-old girls(again, μ =
The z distribution and statistics test scores: Imagine that your statistics professor lost all records of students’ raw scores on a recent test. However, she did record students’ z scores for the test, as well as the class average of 41 out of 50 points and the standard deviation of 3 points
inches.a. Calculate the z statistic.b. How does this sample of boys compare to the distribution of sample means?c. What is the percentile rank for this sample?
inches (176.63 centimeters).Remember, μ =
Heights of boys and the z statistic: Imagine a basketball team that comprises thirteen 15-year-old boys. The average height of the team is
inches.a. Calculate the z statistic.b. How does this sample of girls compare to the distribution of sample means?c. What is the percentile rank for this sample?
inches andσ =
Heights of girls and the z statistic: Imagine a class of thirty-three 15-year-old girls with an average height of 62.60 inches (159.00 centimeters). Remember, μ =
inches.a. Calculate Kona’s z score.b. What is Kona’s percentile score for height?c. What percentage of boys this age are shorter than Kona?d. What percentage of heights are at least as extreme as Kona’s, in either direction?e. If Ian is in the 30th percentile for height as a 15-year-old boy,
Height and the z distribution, question 2: Kona, a 15-yearold boy, is 72 inches (182.88 centimeters) tall. According to the CDC, the average height for boys at this age is
inches.a. Calculate Elena’s z score.b. What percentage of girls are taller than Elena?c. What percentage of girls are shorter?d. How much would Elena have to grow to be perfectly average?e. If Sarah is in the 75th percentile for height at age 15, how tall is she?f. How much would Elena have to
inches, with a standard deviation of
Height and the z distribution, question 1: Elena, a 15-year-old girl, is 58 inches (147.32 centimeters) tall. The Centers for Disease Control and Prevention (CDC) indicates that the average height for girls at this age is
as the population standard deviation.a. Australia’s unemployment rate was 5.4. Calculate the percentile for Australia—that is, what percentage is less than that of Australia?b. The UK’s unemployment rate was 8.5. Calculate its percentile—that is, what percentage is less than that of the
Percentiles and unemployment rates: The U.S. Bureau of Labor Statistics’ annual report published in 2011 provided adjusted unemployment rates for 10 countries. The mean was 7%, and the standard deviation was 1.85. For the following calculations, treat 7% as the population mean and
You are conducting a z test on a sample for which you observe a mean weight of 150 pounds. The population mean is 160, and the standard deviation is 100.a. Calculate a z statistic for a sample of 30 people.b. Repeat part (a) for a sample of 300 people.c. Repeat part (a) for a sample of 3000 people.
and an alpha level of approximately 0.10, or 10%. For each of the following values, determine whether you would reject or fail to reject the null hypothesis:a. z = 0.95b. z =−1.77c. A z statistic that 2% of the scores fall above
Use the cutoffs of −1.65 and
If the cutoffs for a z test are −2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases:a. z =−0.94b. z = 2.12c. A z score for which 49.6% of the data fall between z and the mean

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