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essentials of statistics

Questions and Answers of Essentials Of Statistics

6.53 The z distribution and a rogue cardiologist: A cardiologist in Munster, Indiana, was accused of performing unnecessary heart surgeries (Cresswell, 2015). Investigators found that the rates for
6.52 Percentiles, raw scores, and credit card theft: Credit card companies will often call cardholders if the pattern of use indicates that the card might have been stolen. Let’s say that you
6.51 A distribution of means and the General Social Survey: Refer to Exercise 6.49. Again, pretend that the GSS sample is the entire population of interest.a. Imagine that you randomly selected 80
6.50 A distribution of scores and the General Social Survey: Refer to the previous exercise. Again, pretend that the GSS sample is the entire population of interest.a. Imagine that you randomly
6.49 Distributions and the General Social Survey: The General Social Survey (GSS) is a survey of approximately 2000 U.S. adults conducted each year since 1972, for a total of more than 38,000
6.48 Distributions, personality testing, and social introversion: See the description of the MMPI-2 in the previous exercise. The mean T score is always 50, and the standard deviation is always 10.
6.47 Distributions, personality testing, and depression: The revised version of the Minnesota Multiphasic Personality Inventory (MMPI-2) is the most frequently administered self-report personality
6.46 Distributions and life expectancy: Researchers have reported that the projected life expectancy for South African men diagnosed with human immunodeficiency virus (HIV) at age 20 who receive
6.45 Raw scores, z scores, percentiles, and sports teams: Let’s look at baseball and football again. We’ll look at data for all of the teams in Major League Baseball (MLB) and the National
6.44 The z distribution and comparing scores on two tests of English language learning: The Test of English as a Foreign Language (TOEFL), with scores ranging from 0 to 120, has traditionally been
6.43 z scores and comparisons of sports teams: A common quandary faces sports fans who live in the same city but avidly follow different sports. How does one determine whose team did better with
6.42 Percentiles and eating habits: As noted in How It Works 6.1, Georgiou and colleagues (1997) reported that college students had healthier eating habits, on average, than did those individuals who
6.41 The normal curve in the media: Statistics geeks rejoiced when the New York Times published an article on the normal curve (Dunn, 2013)! Biologist Casey Dunn wrote that “Many real-world
6.40 The normal curve and real-life variables, part II: For each of the following variables, state whether the distribution of scores would likely approximate a normal curve. Explain your answer.a.
6.39 The normal curve and real-life variables, part I: For each of the following variables, state whether the distribution of scores would likely approximate a normal curve. Explain your answer.a.
6.38 Converting z scores to raw CFC scores: A study using the Consideration of Future Consequences scale found a mean CFC score of 3.20, with a standard deviation of 0.70, for the 800 students in the
6.37 z statistics and CFC scores: We have already discussed summary parameters for CFC scores for the population of participants in a study by Adams (2012). The mean CFC score was 3.20, with a
6.36 The z distribution applied to admiration ratings: A sample of 148 of our statistics students rated their level of admiration for Hillary Clinton on a scale of 1 to 7. The mean rating was 4.06,
6.35 The z distribution and hours slept: A sample of 150 statistics students reported the typical number of hours that they sleep on a weeknight. The mean number of hours was 6.65, and the standard
6.34 z scores and the GRE: By design, the verbal subtest of the GRE has a population mean of 500 and a population standard deviation of 100 (the quantitative subtest has the same mean and standard
6.33 Distributions and getting ready for a date: We asked 150 students in our statistics classes how long, in minutes, they typically spend getting ready for a date. The scores ranged from 1 minute
6.32 Normal distributions in real life: Many variables are normally distributed, but not all are. (Fortunately, the central limit theorem saves us when we conduct research on samples from non-normal
6.31 A sample of 100 people had a mean depression score of 85; the population mean for this depression measure is 80, with a standard deviation of 20. A different sample of 100 people had a mean
6.30 Compute a z statistic for each of the following, assuming the population has a mean of 100 and a standard deviation of 20:a. A sample of 43 scores has a mean of 101.b. A sample of 60 scores has
6.29 A population has a mean of 55 and a standard deviation of 8. Compute μM and σM for each of the following sample sizes:a. 30b. 300c. 3000
6.28 Compute the standard error (σM) for each of the following sample sizes, assuming a population mean of 100 and a standard deviation of 20:a. 45b. 100c. 4500
6.27 Assume a normal distribution when answering the following questions.a. What percentage of scores falls below the mean?b. What percentage of scores falls between 1 standard deviation below the
6.26 Compare the following scores:a. A score of 811 when μ = 800 and σ = 29 against a score of 4524 when μ = 3127 and σ = 951b. A score of 17 when μ = 30 and σ = 12 against a score of 67 when
6.25 Using the instructions in Example 6.9, compare the following “apples and oranges”: a score of 45 when the population mean is 51 and the standard deviation is 4, and a score of 732 when the
6.24 A study of the Consideration of Future Consequences (CFC) scale found a mean score of 3.20, with a standard deviation of 0.70, for the 800 students in the sample (Adams, 2012). (Treat this
6.23 By design, the verbal subtest of the Graduate Record Examination (GRE) has a population mean of 500 and a population standard deviation of 100. Convert the following z scores to raw scores using
6.22 By design, the verbal subtest of the Graduate Record Examination (GRE) has a population mean of 500 and a population standard deviation of 100. Convert the following z scores to raw scores
6.21 For a population with a mean of 1179 and a standard deviation of 164, convert each of the following z scores to raw scores.a. −0.23b. 1.41c. 2.06d. 0.03
6.20 For a population with a mean of 250 and a standard deviation of 47, convert each of the following z scores to raw scores.a. 0.54b. −2.66c. −1.00d. 1.79
6.19 For a population with a mean of 250 and a standard deviation of 47, calculate the z scores for 203 and 297. Explain the meaning of these values.
6.17 A population has a mean of 1179 and a standard deviation of 164. Calculate z scores for each of the following raw scores:a. 1000b. 721c. 1531d. 1184 6.18 For a population with a mean of 250 and
6.16 A population has a mean of 250 and a standard deviation of 47. Calculate z scores for each of the following raw scores:a. 391b. 273c. 199d. 160d. What do you observe happening across these three
6.15 Create a histogram for these three sets of scores. Each set of scores represents a sample taken from the same population.a. 6 4 11 7 7b. 6 4 11 7 7 2 10 7 8 6 6 7 5 8c. 6 4 11 7 7 2 10 7 8 6 6 7
6.14 Each of the following equations has an error. Identify, fix, and explain the error in each of the following equations.a. σM = μ √Nb. z = (μ − μM) σM (for a distribution of means)c. z =
6.13 What does a z statistic—a z score based on a distribution of means —tell us about a sample mean?
6.12 Why does the standard error become smaller simply by increasing the sample size?
6.11 What is the difference between standard deviation and standard error?
6.10 What does the symbol σM stand for?
6.9 What does the symbol μM stand for?
6.8 Why is the central limit theorem such an important idea for dealing with a population that is not normally distributed?
6.7 What are the mean and the standard deviation of the z distribution?
6.6 Give three reasons why z scores are useful.
6.5 What is a z score?
6.4 Explain how the word standardize is used in everyday conversation, then explain how statisticians use it.
6.3 How does the size of a sample of scores affect the shape of the distribution of data?
6.2 What point on the normal curve represents the most commonly occurring observation?
6.1 Explain how the word normal is used in everyday conversation, then explain how statisticians use it.
5.65 Preregistration, crowdsourcing, and fake news: Ethical researchers are increasingly using the Internet to modernize their research and conduct it in a more ethical way. In one study, not yet
5.64 Treatment for depression: Researchers conducted a study of 18 patients whose depression had not responded to treatment (Zarate, 2006). Half received one intravenous dose of ketamine, a
5.63 Alcohol abuse interventions: Sixty-four male students were ordered, after they had violated university alcohol rules, to meet with a school counselor. Borsari and Carey (2005) randomly assigned
5.62 Horoscopes and predictions: People remember when their horoscopes had an uncanny prediction—say, the prediction of a problem in love on the exact day of the breakup of a romantic
5.61 Testimonials and Harry Potter: Amazon and other online bookstores offer readers the opportunity to write their own book reviews, and many potential readers scour these reviews to decide which
5.60 Probability and sumo wrestling: In their book Freakonomics, Levitt and Dubner (2005) describe a study conducted by Duggan and Levitt (2002) that broached the question: Do sumo wrestlers cheat?
5.59 Confirmation bias, errors, replication, and horoscopes: A horoscope on Astrology.com stated: “A big improvement is in the works, one that you may know nothing about, and today is the day for
5.58 Rejecting versus failing to reject an invitation: Imagine you have found a new study partner in your statistics class. One day, your study partner asks you to go on a date. This invitation takes
5.57 Type I versus Type II errors: Examine the statements from the previous exercise repeated here. For each, if this conclusion were incorrect, what type of error would the researcher have made?
5.56 Decision about null hypotheses: For each of the following fictional conclusions, state whether the researcher seems to have rejected or failed to reject the null hypothesis (contingent, of
5.55 Null hypotheses and research hypotheses: For each of the following studies, cite the likely null hypothesis and the likely research hypothesis.a. A forensic cognitive psychologist wondered
5.54 Independent or dependent trials and probability: Gamblers often falsely predict the outcome of a future trial based on the outcome of previous trials. When trials are independent, the outcome of
5.53 Independent trials and the U.S. presidential election: Nate Silver is a statistician and journalist who uses statistics to create prediction tools. In an article leading up to the 2012 U.S.
5.52 Independent trials and Eurovision Song Contest bias: As reported in the Telegraph (Highfield, 2005), Oxford University researchers investigated allegations of voting bias in the annual
5.51 Probability, proportion, percentage, and Where’s Waldo?: Slate.com reporter Ben Blatt (2013) analyzed the location of Waldo in the game in which you must find Waldo, a cartoon man who always
5.50 Probability and coin flips: Short-run proportions are often quite different from long-run probabilities.a. In your own words, explain why we would expect proportions to fluctuate in the short
5.49 Confirmation bias and negative thought patterns: Explain how the general tendency of a confirmation bias might make it difficult to change negative thought patterns that accompany major
5.48 Random sampling or random assignment: For each of the following hypothetical scenarios, state whether sampling or assignment is being described. Is the method of sampling or assignment random?
5.47 Samples and a survey on sex education: The Gizmodo blog Throb, a Web site focused on the science of sex, released its own sex education survey (Kelly, 2015). The journalist who developed the
5.46 Samples and Cosmo quizzes: Cosmopolitan magazine (Cosmo, as it’s known popularly) publishes many of its wellknown quizzes on its Web site. One quiz, aimed at heterosexual women, is titled
5.45 Online sampling and visualizing neurons: Researcher Zoran Popović has developed a video game called Mozak (SerboCroatian for “brain”) for the Allen Institute for Brain Science that enlists
5.44 Random sampling and random assignment: For each of the following studies, state (1) whether random sampling was likely to have been used, and explain whether it would have been possible to use
5.43 Random sampling and a survey of psychology majors: Imagine that you have been hired by the psychology department at your school to administer a survey to psychology majors about their
5.42 Negativity bias and WEIRD: Refer to the description of the study by Amber Boydstun and her colleagues (2019) in the previous exercise. How is the COG statement provided by the authors related to
5.44 Random sampling and random assignment: For each of the following studies, state (1) whether random sampling was likely to have been used, and explain whether it would have been possible to use
5.42 Negativity bias and WEIRD: Refer to the description of the study by Amber Boydstun and her colleagues (2019) in the previous exercise. How is the COG statement provided by the authors related to
5.41 Negativity bias and constraints on generality: In a recent article, Amber Boydstun and her colleagues (2019) described a study on the effects of negativity bias in a political context.
5.40 Random assignment and the school psychologist career survey: Refer to the previous exercise when responding to the following questions.a. Describe how the researcher would randomly assign the
5.39 Hypotheses and the school psychologist career survey: Continuing with the study described in the previous exercise, once the researcher had randomly selected the sample of 100 Canadian
5.38 Random sampling and a school psychologist career survey: Imagine that the Canadian government reported that there are 7550 psychologists working in Canada. A researcher wants to randomly sample
5.37 Random numbers and PINs: How random is your personal identification number or PIN? Your PIN is one of the most important safeguards for the accounts that hold your money and valuable information
5.36 Coincidence and the lottery: “Woman wins millions from Texas lottery for 4th time” read the headline about Joan Ginther’s amazing luck (Wetenhall, 2010). Two of the tickets were from the
5.35 Indicate whether each of the following statements refers to personal probability or to expected relative-frequency probability. Explain your answers.a. The chance of a die showing an even number
5.34 Convert the following percentages to proportions:a. 87.3%b. 14.2%c. 1%
5.33 Convert the following percentages to proportions:a. 62.7%b. 0.3%c. 4.2%
5.32 Convert the following proportions to percentages:a. 0.0173b. 0.8c. 0.3719
5.31 On a game show, 8 people have won the grand prize and a total of 266 people have competed. Estimate the probability of winning the grand prize.
5.30 What is the probability of hitting a target if, in the long run, 71 out of every 489 attempts actually hit the target?
5.29 Explain why, given the general tendency people have of perceiving illusory correlations, it is important to collect objective data.
5.28 Explain why, given the general tendency people have of exhibiting the confirmation bias, it is important to collect objective data.
5.27 You are running a study with five conditions, numbered 1 through 5. Using an online random numbers generator, assign the first seven participants who arrive at your lab to conditions, not
5.26 Randomly assign eight people to three conditions of a study, numbered 1, 2, and 3 using an online random numbers generator. (Note: Assign people to conditions without concern for having an equal
5.25 Airport security makes random checks of passenger bags every day. If 1 in every 10 passengers is checked, use an online random numbers generator to determine the first 6 people to be
5.24 Forty-three tractor-trailers are parked for the night in a rest stop along a major highway. You assign each truck a number from 1 to 43. Use an online random numbers generator to select four
5.23 What is the difference between a Type I error and a Type II error?
5.22 What are the two decisions or conclusions we can make about our hypotheses, based on the data?
5.21 What is the difference between a null hypothesis and a research hypothesis?
5.20 One step in hypothesis testing is to randomly assign some members of the sample to the control group and some to the experimental group. What is the difference between these two groups?

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