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Essentials Of Statistics For The Behavioral Sciences 4th Edition Susan A. Nolan, Thomas Heinzen - Solutions

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 100.1. Calculate a z statistic for a sample of 30 people.2. Repeat part (a) for a sample of 300 people.3. Repeat part (a) for a sample of 3000 people.
Use the cutoffs of −1.65 and 1.65 and a p 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:1. z = 0.95 2. z = −1.77 3. A z statistic that 2% of the scores fall above
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:1. z = −0.94 2. z = 2.12 3. A z score for which 49.6% of the data fall between z and the mean
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:1. z = 1.06 2. z = −2.06 3. A z score beyond which 7% of the data fall in each tail
You are conducting a z test on a sample of 132 people for whom you observed a mean SAT verbal score of 490. The population mean is 500, and the standard deviation is 100. Calculate the mean and the spread of the comparison distribution (μM and σM).
You are conducting a z test on a sample of 50 people with an average SAT verbal score of 542 (assume we know the population mean to be 500 and the standard deviation to be 100). Calculate the mean and the spread of the comparison distribution (μM and σM).
State the percentage of scores in a one-tailed critical region for each of the following p levels:1. 0.05 2. 0.10 3. 0.01
For each of the following p levels, what percentage of the data will be in each critical region for a two-tailed test?1. 0.05 2. 0.10 3. 0.01
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?
Rewrite each of the following probabilities, or p levels, as percentages:1. 0.19 2. 0.04 3. 0.92
Rewrite each of the following percentages as probabilities, or p levels:1. 5%2. 83%3. 51%
Using the z table in Appendix B, calculate the following percentages for a z score of 1.71:1. Above this z score 2. Below this z score 3. At least as extreme as this z score
Using the z table in Appendix B, calculate the following percentages for a z score of −0.08:1. Above this z score 2. Below this z score 3. At least as extreme as this z score
Calculate the following percentages for a z score of 0.74, with a tail of 22.96%:1. What percentage of scores falls below this z score?2. What percentage of scores falls between the mean and this z score?3. What proportion of scores falls below a z score of −0.74?
Calculate the following percentages for a z score of −1.61, with a tail of 5.37%:1. What percentage of scores falls above this z score?2. What percentage of scores falls between the mean and this z score?3. What proportion of scores falls above a z score of 1.61?
If an effort to replicate a study fails, what are two things that the failure could indicate about the original study?
What is replication and why is it important for behavioral science research?
Write the symbols for the null hypothesis and research hypothesis for a one-tailed test.
Why do researchers typically use a two-tailed test rather than a one-tailed test?
What is the difference between a one-tailed hypothesis test and a twotailed hypothesis test in terms of critical regions?
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.
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 in order for a researcher to reject the null hypothesis.
What do these symbolic expressions mean: H0: μ1 = μ2 and H1: μ1 ≠ μ2?
What does statistically significant mean to statisticians?
What is the standard size of the critical region used by most statisticians?
What are critical values and the critical region?
What are the six steps of hypothesis testing?
What is the difference between parametric tests and nonparametric tests?
What sample size is recommended in order to meet the assumption of a normal distribution of means, even when the underlying population of scores is not normal?
In statistics, what do we mean by assumptions?
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?
How do we calculate the percentage of scores below a particular positive z score?
When we look up a z score on the z table, what information can we report?
What is a percentile?
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 culture. In a recent article (Hickey, 2015), the author uses z scores to standardize book reviews from
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 suspiciously strong performances on standardized tests that often mysteriously declined the following year when a
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 deviation of 10.98.Let’s say that you decide to use the GSS data to test whether people who live in
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 clearing out arteries and that leads to higher profits for doctors than do the other two procedures.The
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 metropolitan police force, he is known as a ‘super recognizer’” (Bennhold, 2015). Prosopagnosia, also
The z distribution and a rogue cardiologist: A cardiologist in Munster, Indiana, has been accused of conducting unnecessary heart surgeries(Creswell, 2015). Investigators found that the rates for one heart procedure were in the top 10% in the country for the city where this doctor worked.Lawyers
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 charge an average of $280 a month on your credit card, with a standard deviation of $75. The credit card
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.1. Imagine that you randomly selected 80 people from this population, and that they had a mean of 8.7. Would you compare this sample mean to a
A distribution of scores and the General Social Survey: Refer to Exercise 6.49. Again, pretend that the GSS sample is the entire population of interest.1. Imagine that you randomly selected one person from this population who reported that he had 18 close friends. Would you compare his score to a
Distributions and the General Social Survey: The General Social Survey (GSS) is a survey of approximately 2000 adults conducted each year since 1972, for a total of more than 38,000 participants. During several years of the GSS, participants were asked how many close friends they have. The mean for
Distributions, personality testing, and social introversion: See the description of the MMPI-2 in Exercise 6.47. The mean T score is always 50, and the standard deviation is always 10. Imagine that you administer the MMPI-2 to 50 respondents who do not use Instagram or any other social media; you
Distributions, personality testing, and depression: The revised version of the Minnesota Multiphasic Personality Inventory (MMPI-2) is the most frequently administered self-report personality measure. Test-takers respond to more than 500 true/false statements, and their responses are scored,
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 antiretroviral therapy(ART) is 27.6 years (Johnson et al., 2013). Imagine that the researchers determined
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 Football League (NFL), respectively.1. In 2012, the mean number of wins for MLB teams was 81.00, with a
z scores and comparisons of admiration ratings: Our statistics students were asked to rate their admiration of Hillary Clinton on a scale of 1 to 7.They also were asked to rate their admiration of actor, singer, and former American Idol judge Jennifer Lopez and their admiration of tennis player
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 respect to its league division?In 2012, the Atlanta Braves baseball team and the Atlanta Falcons football
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 who were neither college students nor college graduates. The 412 students in the study ate breakfast a mean of 4.1 times
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 observations can be approximated by, and tested against, the same expected pattern: the normal distribution.”
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.1. Number of minutes that students check Facebook and other social media each week 2. Volume of water that
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.1. Number of movies that a college student watches in a year 2. Number of full-page advertisements in a
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 sample (Adams, 2012).1. Imagine that your z score on the CFC score is −1.2. What is your raw score?
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 standard deviation of 0.70. (Remember that we treated the sample of 800 participants as the entire population.)
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, and the standard deviation was 1.70.(For this exercise, treat this sample as the entire population of
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 deviation was 1.24. (For this exercise, treat this sample as the entire population of interest.)1. What is
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 deviation).1. Use symbolic notation to state the mean and the standard deviation of the GRE verbal test.2.
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 to 120 minutes, and the mean was 51.52 minutes. Here are the data for 40 of these students:30 90 60 60 5
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 nonnormal populations if the samples are larger than 30!) Which of the following are likely to be normally
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 score of 17 on a different depression measure; the population mean for this measure is 15, with a standard
Compute a z statistic for each of the following, assuming the population has a mean of 100 and a standard deviation of 20:1. A sample of 43 scores has a mean of 101.2. A sample of 60 scores has a mean of 96.3. A sample of 29 scores has a mean of 100.
A population has a mean of 55 and a standard deviation of 8. Compute μM and σM for each of the following sample sizes:1. 30 2. 300 3. 3000
Compute the standard error (σM) for each of the following sample sizes, assuming a population mean of 100 and a standard deviation of 20:
Assume a normal distribution when answering the following questions.1. What percentage of scores falls below the mean?2. What percentage of scores falls between 1 standard deviation below the mean and 2 standard deviations above the mean?3. What percentage of scores lies beyond 2 standard
Compare the following scores:1. A score of 811 when μ = 800 and σ = 29 against a score of 4524 when μ = 3127 and σ =951 2. A score of 17 when μ = 30 and σ = 12 against a score of 67 when μ = 88 and σ = 16
Using the instructions on p. 145, 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 population mean is 765 and the standard deviation is 23.1. Convert these scores to standardized scores.2. Using
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 sample as the entire population of interest.)1. If the CFC score is 4.2, what is the z score? Use symbolic
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 symbolic notation and the formula.1. 1.5 2. −0.5
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 without using a formula.1. 1.5 2. −0.5 3. −2.0
For a population with a mean of 1179 and a standard deviation of 164, convert each of the following z scores to raw scores.1. −0.23 2. 1.41 3. 2.06 4. 0.03
For a population with a mean of 250 and a standard deviation of 47, convert each of the following z scores to raw scores.1. 0.54 2. −2.66 3. −1.00 4. 1.79
A population has a mean of 1179 and a standard deviation of 164.Calculate z scores for each of the following raw scores:1. 1000 2. 721 3. 1531 4. 1184
A population has a mean of 250 and a standard deviation of 47. Calculate z scores for each of the following raw scores:1. 391 2. 273 3. 199
Create a histogram for these three sets of scores. Each set of scores represents a sample taken from the same population.1. 6 4 11 7 7 2. 6 4 11 7 7 2 10 7 8 6 6 7 5 8 3.6 4 11 7 7 2 10 7 8 6 6 7 5 8 7 8 9 7 6 9 3 9 5 6 8 11 8 3 8 4 10 8 5 5 8 9 9 7 8 7 10 7 4. What do you observe happening across
Each of the following equations has an error. Identify, fix, and explain the error in each of the following equations.1. σM=μN 2. z=(μ−μM)σM (for a distribution of means)3. z=(M−μM)σ (for a distribution of means)4. z=(X−μ)σM (for a distribution of scores)
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 hypothesized quick fix for depression;half received one intravenous dose of placebo. Far more of the patients who
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 these students to one of two conditions. Those in the first condition were assigned to undergo a newly
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 relationship—and decide that horoscopes are accurate. Munro & Munro (2000) are among those who have challenged such
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 books to buy. Harry Potter books attract a great deal of these reader reviews. One Amazon reviewer, “bel
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? Sumo wrestlers garner enormous respect in Japan, where sumo wrestling is considered the national sport. The
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 the big unveiling.” A jobseeking recent college graduate might spot some new listings for interesting
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 you completely by surprise, and you have no idea what to say. You are not attracted to the person in a
Type I versus Type II errors: Examine the statements from Exercise 5.50, repeated here. For each, if this conclusion were incorrect, what type of error would the researcher have made? Explain your answer.
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 course, on inferential statistics having backed up the statement). Explain the rationale for your decision.
Null hypotheses and research hypotheses: For each of the following studies, cite the likely null hypothesis and the likely research hypothesis.1. A forensic cognitive psychologist wondered whether repetition of false information(versus no repetition) would increase the tendency to develop false
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 a future trial cannot be predicted based on the outcomes of previous trials. For each of the following
Independent trials and the U.S. presidential election: Nate Silver is a statistician and journalist well known for his accurate prediction tools. In an article leading up to the 2012 U.S. presidential election in which Barack Obama bested Mitt Romney, Silver (2012) explained his prediction methods
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 Eurovision Song Contest, which pits pop music acts from across Europe, one per country, against each other. The
Probability, proportion, percentage, and Where’s Waldo?: Salon.com reporter Ben Blatt analyzed the location of Waldo in the game in which you must find Waldo, a cartoon man who always wears a redand-white-striped sweater and hat, in a highly detailed illustration (2013). Blatt reported that “53
Probability and coin flips: Short-run proportions are often quite different from long-run probabilities.
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 Depressive Disorder.
Random selection or random assignment: For each of the following hypothetical scenarios, state whether selection or assignment is being described. Is the method of selection or assignment random? Explain your answer.
Samples and a survey on sex education: The Gizmodo blog Throb, a Web site focused on the science of sex, released their own sex education survey (Kelly, 2015). The journalist who developed the survey wrote: “I hope that with enough of your answers, we can start to build a picture of what sex ed
Samples and Cosmo quizzes: Cosmopolitan magazine (Cosmo, as it’s known popularly) publishes many of its well-known quizzes on its Web site.One quiz, aimed at heterosexual women, is titled “Are You Way Too Obsessed with Your Ex?” A question about “your rebound guy” offers these three
Volunteer samples and a college football poll: A volunteer sample is a kind of convenience sample in which participants select themselves to participate. One recent year, USA Today published an online poll on its Web site asking this question about U.S. college football: “Who is your pick to win
Random selection and random assignment: For each of the following studies, state (1) whether random selection was likely to have been used, and explain whether it would have been possible to use it. Also, describe the population to which the researcher wanted to and could generalize, and state(2)
Random selection 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 experiences in the department. You have been asked to randomly select 60 of these majors from the overall pool of
Random assignment and the school psychologist career survey: Refer to Exercises 5.34 and 5.35 when responding to the following questions.1. Describe how the researcher would randomly assign the participants to the levels of the independent variable. Be sure to explain how the levels of the

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