On an exam with a mean of M = 40, you obtain a score of X = 35. a. Relative to other students, would your performance on the exam be better with a standard deviation of s = 2 or with a standard deviation of s = 8? (Hint: Sketch each distribution and find the location of your score.) b. If your score were X = 46, would you prefer s = 2 or s = 8? Explain your answer.
> What information is available about the scores in a regular frequency distribution table that you cannot obtain for the scores in a grouped table?
> Positive events are great, but recent research suggests that unexpected positive outcomes (e.g., an unseasonably sunny day) predict greater-than-normal amounts of risk-taking and gambling (Otto, Fleming, & Glimcher, 2016). Researchers demonstrated th
> Anxiety affects our ability to make decisions. Remmers and Zander (2018) demonstrated that anxiety also prevents us from intuiting about our environments. In their experiment, 111 participants were randomly assigned to receive either an anxiety-inducing
> Recent research has shown that creative people are more likely to cheat than their less-creative counterparts (Gino & Ariely, 2012). Participants in the study first completed creativity assessment questionnaires and then returned to the lab several d
> Find the t value that forms the boundary of the critical region in the right-hand tail for a two-tailed test with α = .05 for each of the following sample sizes. a. n = 9 b. n = 16 c. n = 36 d. Repeat parts a–c assuming a one-tailed test, α = .05. e. Rep
> The following sample of n = 5 scores was obtained from a population with unknown parameters. Scores: 20, 25, 30, 20, 30 a. Compute the sample mean and variance. (Note: These are descriptive values that summarize the sample data.) b. Compute the estimated
> The Muller-Lyer illusion is shown in the figure. Although the two horizontal lines are the same length, the line on the left appears to be much longer. To examine the strength of this illusion, Gillam and Chambers (1985) recruited 10 participants who rep
> In a classic study of procrastination by Lay (1986), in an introductory psychology class, students received a survey that measured procrastination. Participants were instructed to complete the survey and return it to the researcher by mail. High-procrast
> Oishi and Schimmack (2010) report that people who move from home to home frequently as children tend to have lower than average levels of well-being as adults. To further examine this relationship, a psychologist obtains a sample of n = 12 young adults w
> Your subjective experience of time is not fixed. You experience time “flying” during some activities and “dragging” during others. Researchers have shown that your experience of time can be altered by drugs that interact with the brain regions that are r
> To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of μ = 50, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 55. a. Assuming that the
> For the following set of scores, find the value of each expression:
> To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 20, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 22 with a variance of s2 = 9. a.
> People are poor at making judgments about probability. One source of error in judgments of probability is the base rate fallacy in which people ignore the base rates of low probability events. In a study of the base rate fallacy by Bar-Hillel (1980), par
> Weinstein, McDermott, and Roediger (2010) report that students who were given questions to be answered while studying new material had better scores when tested on the material compared to students who were simply given an opportunity to reread the mater
> To evaluate the effect of a treatment, a sample of n = 6 is obtained from a population with a mean of μ = 80, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 72. a. If the sample var
> To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 44.5 with a variance of s2 = 36.
> A random sample of n = 4 individuals is selected from a population with μ = 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 40.1 with SS = 48. a. How much difference is there betwe
> A random sample of n = 7 individuals is selected from a population with μ = 50, and a treatment is administered to each individual in the sample. After treatment, the following scores are observed: 37 49 47 47 47 43 45 a. Compute the sample mean an
> A random sample of n 5 9 individuals is selected from a population with m 5 20, and a treatment is administered to each individual in the sample. After treatment, the following scores are observed: 43 15 37 17 29 21 25 29 27 a. Compute the sample
> The National Study of Student Engagement (Indiana University, 2018) reports that the average, full-time college senior in the United States spends only μ = 15, s 5 9, hours per week preparing for classes by reading, doing homework, studying, etc. A state
> According to the CDC (2016), the average life expectancy of someone with diabetes is μ = 72 years, s = 14. Suppose that a sample of n = 64 people diagnosed with diabetes who received a blood glucose monitoring implant had an average life expectancy of M
> For the following set of scores, find the value of each expression:
> Define a Type I error and a Type II error and explain the consequences of each. Which type of error is worse? Why?
> Suppose that a researcher is interested in the effect of an exercise program on body weight among men. The researcher expects a treatment effect of 3 pounds after 15 weeks of exercise in the exercise program. In the population, the mean adult body weight
> Research has shown that IQ scores have been increasing for years (Flynn, 1984, 1999). The phenomenon is called the Flynn effect and the data indicate that the increase appears to average about 7 points per decade. To examine this effect, a researcher obt
> Telles, Singh, and Balkrishna (2012) reported that yoga training improves finger dexterity. Suppose that a researcher conducts an experiment evaluating the effect of yoga on standardized O’Conner finger dexterity test scores. A sample of n = 4 participan
> A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of μ = 50 and a standard deviation of s = 10. The researcher expects a 15-point treatment effect and plans to use a two-tai
> After examining over one million online restaurant reviews and the associated weather conditions, Bakhshi, Kanuparthy, and Gilbert (2014) reported significantly higher ratings during moderate weather compared to very hot or very cold conditions. To verif
> Screen time and use of social media are related to negative mental health outcomes, including suicidal thoughts (Twenge, Joiner, Rogers, & Martin, 2018). In a national survey of adolescents, the mean number of depressive symptoms was μ = 2.06, σ = 1.00.
> A high school teacher has designed a new course intended to help students prepare for the mathematics section of the SAT. A sample of n = 20 students is recruited for the course and, at the end of the year, each student takes the SAT. The average score f
> Researchers at a weather center in the northeastern United States recorded the number of 90° Fahrenheit days each year since records first started in 1875. The numbers form a normal-shaped distribution with a mean of μ = 9.6 and a standard deviation of s
> A random sample is selected from a normal population with a mean of μ = 40 and a standard deviation of σ = 10. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 46. a. How large a sample is necessary f
> For the following set of scores, find the value of each expression:
> Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6
> A random sample of n = 9 scores is selected from a normal population with a mean of μ = 100. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 106. a. If the population standard deviation is σ = 10, is
> A random sample is selected from a normal population with a mean of μ = 20 and a standard deviation of σ = 10. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 25. a. If the sample consists of n = 25
> Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Kawachi, 2006). In a representative study, a sample of n = 100 adolescents with
> Ackerman and Goldsmith (2011) report that students who study from a screen (smartphone, tablet, or computer) tended to have lower quiz scores than students who studied the same material from printed pages. To test this finding, a professor identifies a s
> The personality characteristics of business leaders (e.g., CEOs) are related to the operations of the businesses that they lead (Oreg & Berson, 2018). Traits like openness to experience are related to positive financial outcomes and other traits are rela
> Compare the following: a. Measures of variability, s, σ, and σ M b. Measures of central tendency, M, μ, and μ M
> Suppose that a researcher developed a drug that she claims increases extroversion. A sample of n = 4 participants has a sample mean of M = 115 on a personality assessment after taking the drug. The personality test has a population mean of μ = 100 and σ
> A normal distribution has a mean of μ = 60 and a standard deviation of σ = 12. For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a s
> The distribution exam grades for an introductory psychology class is negatively skewed with a mean of μ = 71.5 and a standard deviation of σ = 12. a. What is the probability of selecting a random sample of n = 9 students with an average grade greater tha
> For random samples of size n = 16 selected from a normal distribution with a mean of μ = 75 and a standard deviation of σ = 20, find each of the following: a. The range of sample means that defines the middle 95% of the distribution of sample means. b. T
> Use summation notation to express each of the following calculations: a. Add the scores and then square the sum. b. Square each score and then add the squared values. c. Subtract 2 points from each score and then add the resulting values. d. Subtract 1 p
> Briefly define each of the following: a. Distribution of sample means b. Central limit theorem c. Expected value of M d. Standard error of M
> A report in 2016 indicates that Americans between the ages of 8 and 18 spend an average of μ = 10 hours per day using some sort of electronic device such as a smartphone computer, or tablet. Assume that the distribution of times is normal with a standard
> Define sampling with replacement and explain why it is used.
> An important reason that students struggle in college is that they are sometimes unaware that they have not yet mastered a new skill. Struggling students often overestimate their level of mastery in part because the skills needed to master a topic are th
> IQ test scores are standardized to produce a normal distribution with a mean of μ = 100 and a standard deviation of σ = 15. Find the proportion of the population in each of the following IQ categories. a. Genius or near genius: IQ over 140 b. Very superi
> A normal distribution has a mean of m 5 70 and a standard deviation of s 5 12. For each of the following scores, indicate whether the body is to the right or left of the score and find the proportion of the distribution located in the body. a. X = 74 b.
> A normal distribution has a mean of m = 50 and a standard deviation of s = 5. For each of the following scores, indicate whether the tail is to the right or left of the score and find the proportion of the distribution located in the tail. a. X = 45 b. X
> The range is completely determined by the two extreme scores in a distribution. The standard deviation, on the other hand, uses every score. a. Compute the range (choose either definition), the variance, and the standard deviation for the following sampl
> A population with a mean of μ = 41 and a standard deviation of σ = 4 is transformed into a standardized distribution with μ = 100 and σ = 20. Find the new, standardized score for each of the following values from the original population. a. X = 39 b. X =
> Use summation notation to express the following calculations. a. Multiply scores X and Y and then add each product. b. Sum the scores X and sum the scores Y and then multiply the sums. c. Subtract X from Y and sum the differences. d. Sum the X scores.
> For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer. a. A score of X = 70 on an exam with μ = 82 and σ 5 8; or a score of X = 60 on an exam with μ = 72 and σ = 12. b. A score of X = 5
> In a sample distribution, a score of X = 21 corresponds to z = -1.00 and a score of X = 12 corresponds to z = -2.50. Find the mean and standard deviation for the sample.
> Solve the following problems. a. After 6 points have been added to every score in a sample, the mean is found to be M = 70 and the standard deviation is s = 13. What were the values for the mean and standard deviation for the original sample? b. After ev
> Calculate SS, σ2, and σ for the following population of N = 4 scores: 0, 6, 6, 8.
> For the following population of scores: 1, 4, 7 a. Calculate the population mean and population variance. b. Complete the following table that lists all possible samples of n = 2 scores from the population. Use the first three rows (Samples aâ€
> For the following sample of n = 10 scores, 6, 5, 4, 3, 3, 3, 2, 2, 2, 1 a. Assume that the scores are measurements of a discrete variable and find the median. b. Assume that the scores are measurements of a continuous variable and find the precise median
> For the following scores, find the value of each expression:
> For a sample of n = 12 scores, what value should be used in the denominator of the formula for variance? What value should be used in the denominator of the formula for the mean? Explain why the two formulas use different values in the denominator.
> Doebel and Munakata (2018) discovered that delay of gratification by children is influenced by social context. All children were told that they were in the “green group” and were placed in a room with a single marshmallow. Participants were told that the
> Dwyer, Figuerooa, Gasalla, and Lopez (2018) showed that learning of flavor preferences depends on the relative value of the reward with which a flavor is paired. In their experiment, rats received pairings of a cherry flavor with 8% sucrose solution afte
> For the following set of scores, find the value of each expression:
> Ackerman and Goldsmith (2011) compared learning performance for students who studied material printed on paper versus students who studied the same material presented on a computer screen. All students were then given a test on the material and the resea
> A survey given to a sample of college students contained questions about the following variables. For each variable, identify the kind of graph that should be used to display the distribution of scores (histogram, polygon, or bar graph). a. Age b. Birth-
> Deters and Mehl (2013) studied the effect of Facebook status updates on feelings of loneliness. Eighty-six participants were randomly assigned to two groups. One group was instructed to post more social media status updates and the other group was not. T
> Calculate the mean for both of the following sets of scores. Use both the computational and definitional formulas to compute SS for both sets of scores. Round to two decimal places for each calculation. Why is there a difference in the calculated SS for
> The results of a recent study showed that children who routinely drank reduced fat milk (1% or skim) were more likely to be overweight or obese at ages 2 and 4 compared to children who drank whole or 2% milk (Scharf, Demmer, & DeBoer, 2013). a. Is this a
> There are two different formulas or methods that can be used to calculate SS. a. Under what circumstances is the definitional formula easy to use? b. Under what circumstances is the computational formula preferred?
> One sample has a mean of M = 6, and a second sample has a mean of M = 12. The two samples are combined into a single set of scores. a. What is the mean for the combined set if both the original samples have n = 4 scores? b. What is the mean for the combi
> Your friend measures the temperature of her coffee to be 70° Celsius. Your friend also notices that the temperature outside is 35° Celsius. Why is it incorrect to say that the coffee is twice as warm as the temperature outside?
> Four scales of measurement were introduced in this chapter, from simple classification on a nominal scale to the more informative measurements from a ratio scale. a. What additional information is obtained from measurements on an ordinal scale compared t
> In a sample of n = 6 scores, five of the scores are each above the mean by one point. Where is the sixth score located relative to the mean?
> Two scores, X and Y, are recorded for each of n 5 5 participants. For these scores, find the value of each expression.
> A tax form asks people to identify their age, annual income, number of dependents, and social security number. For each of these four variables, identify the scale of measurement that probably is used and identify whether the variable is continuous or di
> Explain why honesty is a hypothetical construct instead of a concrete variable. Describe how honesty might be measured and defined using an operational definition.
> A professor is interested in whether student performance on exams is better in the afternoon than in the morning. One sample of students was randomly assigned to receive the exam in the morning and another sample was randomly assigned to receive the exam
> For the following set of scores: a. Construct a frequency distribution table to organize the scores. Include cumulative frequency and cumulative percent. b. What is the percentile rank of the upper real limit of X = 15? c. What is the upper real limit of
> For each of the following, calculate the pooled variance and the estimated standard error for the sample mean difference a. The first sample has n = 4 scores and a variance of s2 = 17, and the second sample has n = 8 scores and a variance of s2 = 27. b.
> In Problem 8, a researcher asked college students to evaluate three new smartphone designs. However, the researcher suspects that college students may have criteria that are different from those used by older adults. To test this hypothesis, the research
> Research indicates that people who volunteer to participate in research studies tend to have higher intelligence than nonvolunteers. To test this phenomenon, a researcher obtains a sample of 200 high school students. The students are given a description
> Suppose that a researcher is interested in differences between young adults and older adults with respect to social media preferences. The researcher asked participants to indicate their preference for a specific social media application by checking all
> Many businesses use some type of customer loyalty program to encourage repeat customers. A common example is the buy-ten-get-one-free punch card. Drèze and Nunes (2006) examined a simple variation of this program that appears to give customer
> Liu et al. (2015) recently reported the results of a study examining whether happy people live longer. The study followed a large sample of British women, aged 50 to 69 over a 10-year period. At the beginning of the study the women were asked several que
> For the following set of scores, find the value of each expression:
> Earlier in the chapter, we introduced the chi-square test of independence with a study examining the relationship between personality and color preference. The following table shows the frequency distribution for a group of n = 200 students who were clas
> With a small sample, a single point can have a large effect on the magnitude of the correlation. To create the following data, we started with the scores from Problem 8 and changed the first X value from X = 3 to X = 8. a. Sketch a scatter plot and estim
> For the following scores, a. Sketch a scatter plot and estimate the value of the Pearson correlation. b. Compute the Pearson correlation.
> The scores below are a modification of the scores in Problem 6: a. Compute SS for X and Y and SP. Compare these values to your answer for part a of Problem 6. b. Compute the Pearson correlation. Compare your results to what you got for part b of Problem
> For the following scores, a. Compute SS for X and Y and SP. b. Compute the Pearson correlation.
> For the following scores, a. Sketch a scatter plot and estimate the Pearson correlation. b. Compute the Pearson correlation.
> For the following scores, a. Sketch a scatter plot and estimate the Pearson correlation. b. Compute the Pearson correlation.
> a. A researcher computes the linear regression equation for a sample of n = 20 pairs of scores, X and Y values. If an analysis of regression is used to test the significance of the equation, what are the df values for the F-ratio? b. A researcher evaluat
> Does the regression equation from Problem 25 account for a significant portion of the variance in the Y scores? Use a = .05 to evaluate the F-ratio. Problem: 25
> a. One set of 10 pairs of scores, X and Y values, produces a correlation of r = 0.60. If SSY = 200, find the standard error of estimate for the regression line. b. A second set of 10 pairs of X and Y values produces a correlation of r = 0.40. If SSY = 20
> For the following set of scores, find the value of each expression:
