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essentials of statistics

Questions and Answers of Essentials Of Statistics

8.46 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
8.45 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
8.44 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,
8.43 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
8.42 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
8.41 Assume you are conducting a meta-analysis over a set of five 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
size you calculated in part (a).
8.40 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
8.39 A meta-analysis reports an average effect size of d = 0.11, with a confidence interval of d =−0.06 to d = 0.28. Would a hypothesis test (assessing the null hypothesis that the average effect
8.38 A meta-analysis reports an average effect size of d = 0.11, with a confidence interval of d = 0.08 to d = 0.14.a. Would a hypothesis test (assessing the null hypothesis that the average effect
8.37 For each of the following z statistics, calculate the p value for a two-tailed test.a. 2.23b. −1.82c. 0.33
8.36 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
8.35 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
8.34 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
8.33 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
8.32 Calculate the effect size for the mean of 1057 observed in the previous exercise, where μ = 1014 and σ = 136.
8.31 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
8.30 Calculate the standard error for each of the following sample sizes when μ = 1014 and σ = 136:a. 12b. 39c. 188
8.29 Calculate the 99% confidence interval for the same fictional data regarding daily TV viewing habits: μ = 4.7 hours; σ = 1.3 hours; sample of 78 people, with a mean of 4.1 hours.
8.28 Calculate the 80% confidence interval for the same fictional data regarding daily TV viewing habits: μ = 4.7 hours; σ = 1.3 hours; sample of 78 people, with a mean of 4.1 hours.
8.27 Calculate the 95% confidence interval for the following fictional data regarding daily TV viewing habits: μ = 4.7 hours; σ = 1.3 hours; sample of 78 people, with a mean of 4.1 hours.
8.26 For each of the following confidence levels, look up the critical z values for a two-tailed z test.a. 80%b. 85%c. 99%
8.25 For each of the following confidence levels, look up the critical z value for a one-tailed z test.a. 80%b. 85%c. 99%
8.24 For each of the following confidence 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%
8.23 For each of the following confidence 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%
8.22 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
8.21 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
8.20 In 2008, a Gallup poll asked people whether they were suspicious of steroid use among Olympic athletes. Thirty-five percent of respondents indicated that they were suspicious when they saw an
8.19 What is the best way to avoid the negative consequences of an underpowered study?
8.18 What are the potential negative consequences of an underpowered study?
8.17 In statistics, concepts are often 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
8.16 Why is it important for a researcher who is conducting a meta-analysis to find not only published studies but also unpublished studies?
8.15 What is the goal of a meta-analysis?
8.14 What are the four basic steps of a meta-analysis?
8.13 Traditionally, what minimum percentage chance of correctly rejecting the null hypothesis is suggested to proceed with an experiment?
8.12 How are statistical power and effect size different but related?
8.11 In your own words, define the word power—first as you would use it in everyday conversation and then as a statistician would use it.
8.10 How does statistical power relate to Type II errors?
8.9 What are Cohen’s guidelines for small, medium, and large effects?
8.8 What does it mean to say an effect-size statistic neutralizes the influence of sample size?
8.7 Relate effect size to the concept of overlap between distributions.
8.6 What effect does increasing the sample size have on standard error and the test statistic?
8.5 In your own words, define the word effect—first as you would use it in everyday conversation and then as a statistician would use it.
8.4 What are the five steps to create a confidence interval for the mean of a z distribution?
8.3 Why do we calculate confidence intervals?
8.2 In your own words, define the word confidence—first as you would use it in everyday conversation and then as a statistician would use it in the context of a confidence interval.
8.1 What specific danger exists when reporting a statistically significant difference between two means?
7.53 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
7.52 The Graded Naming Test and sociocultural differences: Researchers often use z tests to compare their samples to known population norms. The Graded Naming Test (GNT) asks respondents to name
7.51 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
7.50 Power posing, p-hacking, and mixed results: In 2010, a group of researchers published the finding that power posing— adopting a wide stance with one’s hands on one’s hips— improved
7.49 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
7.48 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
7.46 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
7.45 The z distribution and Hurricane Katrina: Hurricane Katrina hit New Orleans on August 29, 2005. The National Weather Service Forecast Office maintains online archives of climate data for all
7.44 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
7.43 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
7.42 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
7.41 The z statistic, distributions of means, and heights of girls: Using what we know about the height of 15-year-old girls (again, μ = 63.80 inches [162.05 centimeters] and σ = 2.66 inches),
7.40 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
7.39 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 69.50 inches (176.63 centimeters). Remember, μ = 67.00
7.38 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 = 63.80 inches and σ = 2.66
7.37 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 67.00 inches, with a
7.36 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
7.35 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
7.34 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
7.33 Use the cutoffs of −1.65 and 1.65 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
7.32 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
7.31 If the cutoffs for a z test are −1.96 and 1.96, determine whether you would reject or fail to reject the null hypothesis in each of the following cases:a. z = 1.06b. z =−2.06c. A z score
7.30 You are conducting a z test on a sample of 132 people for whom you observed a mean verbal score on the SAT, a university admissions test used in the United States and several other countries, of
7.29 You are conducting a z test on a sample of 50 people with an average verbal score on the SAT, a university admissions test used in the United States and several other countries, of 542 (assume
7.28 State the percentage of scores in a one-tailed critical region for each of the following alpha levels:a. 0.05b. 0.10c. 0.01
7.27 For each of the following alpha levels, what percentage of the data will be in each critical region for a two-tailed test?a. 0.05b. 0.10c. 0.01
7.26 If the critical values for a hypothesis test occur where 2.5% of the distribution is in each tail, what are the cutoffs for z?
7.25 Rewrite each of the following probabilities, or alpha levels, as percentages:a. 0.19b. 0.04c. 0.92
7.24 Rewrite each of the following percentages as probabilities, or alpha levels:a. 5%b. 83%c. 51%
7.23 Using the z table in Appendix B, calculate the following percentages for a z score of 1.71:a. Above this z scoreb. Below this z scorec. At least as extreme as this z score
7.22 Using the z table in Appendix B, calculate the following percentages for a z score of −0.08:a. Above this z scoreb. Below this z scorec. At least as extreme as this z score
7.19 What is p-hacking and what are some examples of research behaviors that would constitute p-hacking?
7.18 What is HARKing and why can it be harmful?
7.17 Write the symbols for the null hypothesis and research hypothesis for a one-tailed test.
7.16 Why do researchers typically use a two-tailed test rather than a one-tailed test?
7.15 What is the difference between a one-tailed hypothesis test and a two-tailed hypothesis test in terms of critical regions?
7.14 Using everyday language rather than statistical language, explain why the word cutoff might have been chosen to define the point beyond which we reject the null hypothesis.
7.13 Using everyday language rather than statistical language, explain why the words critical region might have been chosen to define the area in which a z statistic must fall for a researcher to
7.12 What do these symbolic expressions mean: H0: μ1 = μ2 and H1: μ1 ≠ μ2?
7.11 What does statistically significant mean to statisticians?
7.10 What is the standard size of the critical region used by most statisticians?
7.6 What sample size is recommended to meet the assumption of a normal distribution of means, even when the underlying population of scores is not normal? 7.7 What is the difference between
7.5 In statistics, what do we mean by assumptions?
7.4 How is calculating a percentile for a mean from a distribution of means different from doing so for a score from a distribution of scores?
7.3 How do we calculate the percentage of scores below a particular positive z score?
7.2 When we look up a z score on the z table, what information can we report?
#!# 7.1 What is a percentile?
6.59 Cheating in online gaming: Researchers used the normal curve to investigate cheating among online gamers playing a car racing game (Christensen et al., 2013). The graph below shows the winning
6.58 Which was better, the book or the movie: FiveThirtyEight is a popular blog that uses statistics in creative ways to better understand politics, sports, science and health, economics, and
6.57 Cheating on standardized tests: In their book Freakonomics, Levitt and Dubner (2009) describe alleged cheating among teachers in the Chicago public school system. Certain classrooms had
6.56 Rural friendships and the General Social Survey: Earlier, we considered data from the GSS on numbers of close friends people reported having. The mean for this variable is 7.44, with a standard
6.55 Probability and medical treatments: The three most common treatments for blocked coronary arteries are medication, bypass surgery, and angioplasty, which is a medical procedure that involves
6.54 The z distribution and a “super recognizer”: According to a news article, “Friends call Constable [Gary] Collins Rain Man or Yoda or simply The Oracle. But to Scotland Yard, London’s

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