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Questions and Answers of
Statistics
To better understand eating patterns that might contribute to obesity, a researcher measures the average number of calories (per meal) consumed by shift workers (morning, afternoon, night) during two
Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to
Students (freshmen, sophomores, juniors, and seniors) at a local college who were in the same statistics class were given one of three tests (recall, recognition, or a mix of both). Test grades for
To test the relationship between sex and responsiveness to feedback, a group of men and women were given a vignette describing a person of the opposite sex who gave negative, positive, or neutral
A developmental psychologist placed children in a social situation in which they were either rewarded or punished (Factor A: consequence) by a parent, sibling, or stranger (Factor B: type of adult).
Recent studies show that conservative Republican political ideology is associated with greater overall life happiness than liberal Democratic ideology. One potential explanation for this is that
Among other benefits, pets are thought to be great companions that increase satisfaction among pet owners, especially those who would otherwise live alone.A psychologist decides to test this notion.
Define the following key terms:(a) Cell(b) Main effect(c) Interaction
Witt and Schrodt (2006) tested the relationship between nonverbal immediacy (behaviors that enhance closeness and nonverbal interaction with others) and technology. They tested whether teacher
Cheng and Lam (2007) noted that some people think of themselves independently of others (independent self construal), whereas others think of themselves as being part of a larger group
Tung and Deng (2007) studied how emoticons (computerized facial expressions) and sex influenced intrinsic motivation to complete a computer task. Emoticons were used as feedback for responses during
For each example, state whether one correlation is stronger than the other. If one is stronger, then state which is the stronger correlation.(a) r = +.04, r = −.40(b) r = +.50, r = +.23(c) r =
What information does the direction of a correlation coefficient convey?
Möller and Marsh (2013) evaluated the relationship between the verbal and math ability of students (achievement) and their self-belief of their ability (self-concept). In their report, they
Conseur, Hathcote, and Kim (2008) measured the relationship between consumer masculinity and appearance-related self-esteem, consumer masculinity and media influence, and consumer masculinity and
Describe what each of the following statistical terms measures:(a) SSXY(b) √SSXSSY
When does restriction of range limit the interpretation of a significant correlation?
Name four correlation coefficients and describe when it is appropriate to use each.
Which is the predictor variable (X) and which is the criterion variable (Y) for each of the following examples?(a) A researcher tests whether the size of an audience can predict the number of
Distinguish between the predictor variable and the criterion variable.
A health psychologist hypothesizes that students who study more also exercise less because they spend so much time studying. She measures whether the number of hours studying (per week) can predict
A psychologist noted that people have more difficulty sleeping in a bright room than in a dark room. She measured whether the intensity of the light could predict the time it took a sample of four
A psychologist believed that as children get older, they engage in more "inactive activities" such as playing computer games, watching TV, and surfing online. She tested whether there was a
A sports psychologist tested whether the number of team wins in the previous season could predict the number of wins in the following season in a sample of 32 teams. Complete the regression table for
A developmental psychologist tests the extent to which daily intake of fat (in grams) and amount of exercise (in minutes) can predict health (measured using a body mass index [BMI] scale in which
Define the following terms:(a) Slope(b) y-intercept
Describe regression variation in terms of variation in Y.
Describe residual variation in terms of variation in Y.
State three ways that nonparametric tests differ from parametric tests.
For each of the following examples, state whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate, and state the degrees of freedom (df) for the test.(a) An
The Better Business Bureau (BBB) wants to determine whether a certain business is engaging in fair hiring practices. The BBB finds that a local business employs 66 men and 34 women. The general
A local brewery produces three premium lagers named Half Pint, XXX, and Dark Night. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Night. In a marketing test of a
A behavioral therapist records the number of children who are spanked and not spanked by their parents as a form of punishment in a sample of parents who were spanked by their parents as children.
A psychologist studying addiction tests whether cravings for cocaine and relapse are independent or related. The following table lists the observed frequencies in the small sample of people who use
A researcher tests whether the political affiliation of individuals is related to or independent of whether they have positive views of the economy. The researcher records the political affiliations
A professor tests whether the loudness of noise during an exam (low, medium, high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test.(a)
What is Cramer's V for each of the following values for the chi-square test for independence?(a) χ2 = 4.36, N = 80, dfsmaller = 1(b) χ2 = 8.12, N = 120, dfsmaller = 2(c) χ2 = 11.54, N = 150,
Love, Vinson, Tolsma, and Kaufmann (2008) studied the psychological effects of being an undercover officer, including the stress it places on a marriage. The researchers recorded the number of
Yen, Lin, and Chiu (2013) compared the number of male and female people with an intelligence disability (ID) to the proportion of males and females in the general population. In their study, they
In July 2008, an NBC News/Wall Street Journal poll asked a sample of Americans to state which issue (taken from a list) should be the top priority for the U.S. federal government. The following table
Altamura, Dell'Osso, Vismara, and Mundo (2008) measured the relationship between sex and duration of untreated illness (DUI) among a sample of those suffering from major depressive disorder (MDD).
Keskinoglu and colleagues (2007) studied sex discrimination among the elderly. As part of their study, they recorded whether participants were involved in or made decisions concerning personal income
Define the following terms:(a) Frequency observed (fo)(b) Frequency expected (fe)
Name one assumption and one restriction for the chi-square test?
Explain how to interpret the test statistic H.
Why is the variance not meaningful to analyze ordinal scale data?
Use the normal approximation for the Mann-Whitney U test to analyze the data in Question 24 and state whether to retain or reject the null hypothesis.In Question 24With slide show____________________
A psychologist hypothesized that playing music or news radio during work may increase worker productivity. To test this hypothesis, she measured worker productivity (in units per hour) at three
A statistics instructor measured student attitudes toward a statistics course prior to lectures, at the midterm, and after the final exam. Attitudes were measured on a 16-point scale, with higher
Serlin and Harwell (2004) analyzed the power of statistical designs when distributions are not normal. In their article, they reported, "It is well-known that for normally distributed errors
Rojas, Sherrit, Harris, and Knight (2008) conducted a study using the Car, Relax, Alone, Forget, Friends, Trouble (CRAFFT) substance abuse screening test in 14- to 18-year-old patients. This
Lantz (2013) identified that "the Kruskal-Wallis test ... should be the primary [test] used to compare [differences] when it is known that populations are not at least approximately normal". Explain
Which parametric tests do the following tests replace?(a) Sign test(b) Wilcoxon signed-ranks T test(c) Mann-Whitney U test(d) Kruskal-Wallis H test(e) Friedman test
Explain how to interpret the test statistic U.
Explain the difference between a stratified sample and a cluster sample?
In each of the following situations, the sampling frame does not match the population, resulting in under coverage. Give examples of population members that might have been omitted.(a) The population
An important part of employee compensation is a benefits package, which might include health insurance, life insurance, child care, vacation days, retirement plan, parental leave, bonuses, etc.
A random sample of students who use the college recreation center were asked if they approved increasing student fees for all students in order to add a climbing wall to the recreation center.
Greg took a random sample of size 100 from the population of current season ticket holders to State College men’s basketball games. Then he took a random sample of size 100 from the population of
A brief survey regarding opinions about recycling was carefully designed so that the wording of the questions would not influence the responses. Jill administered the survey at a farmer’s market.
The U.S. Department of Justice examined all reported cases of identity theft for U.S. residents aged 16 or older. Their data show that of all the reported incidents of identity theft in a recent
Which technique for gathering data (observational study or experiment) do you think was used in the following studies? Explain.(a) The U.S. Census Bureau tracks population age. In 1900, the
Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on the next page are based on random samples of size 30, 50 and
The following histograms are based on different random samples of size 100 drawn from the same population(i)(ii)(iii)(a) Identify the midpoint of the class with the highest frequency in each of the
The ogives shown are based on U.S. Census data and show the average annual personal income per capita for each of the 50 states. The data are rounded to the nearest thousand dollars.(i) Ogive(ii)
The following data represent glucose blood levels (mg/100 ml) after a 12-hour fast for a random sample of 70 women (Reference: American Journal of Clinical Nutrition, Vol. 19, pp. 345-351). Note:
What percent of undergraduate enrollment in coed colleges and universities in the United States is male? A random sample of 50 such institutions give the following data (Source USA Today allege
The following data represent tonnes of wheat harvested each year (1894-1925) from Plot 19 at the Rothamsted Agricultural Experiment Stations, England.(a) Multiply each data value by 100 to "clear"
The following data represent trunk circumferences (in mm) for a random sample of 60 4-year-old apple trees at East Mailing Agriculture Research Station in England (Reference: S. C. Pearce, University
Critical Thinking Consider the numbers(a) Compute the mode, median, and mean.(b) If the numbers represent codes for the colors of T-shirts ordered from a catalog, which average(s) would make
Critical Thinking Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by 5.(a) Does the mean change? Explain.(b) Does the
Critical Thinking Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by 10.(a) Does the mean change? Explain.(b) Does the
Given the sample datax: 23 17 15 30 25(a) Find the range.(b) Verify that (x - 110 and (x2 - 2568.(c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2
Consider sample data with x̅ = 15 and s = 3.(a) Compute the coefcient of variation.(b) Compute a 75% Chebyshev interval around the sample mean?
Pax World Balanced is a highly respected, socially responsible mutual fund of stocks and bonds (see Viewpoint). Vanguard Balanced Index is another highly regarded fund that represents the entire U.S.
You do not need a lot of money to invest in a mutual fund. However, if you decide to put some money into an investment, you are usually advised to leave it in for (at least) several years. Why?
This is a technique to break down the variation of a random variable into useful components (called stratum) in order to decrease experimental variation and increase accuracy of results. It has been
Three local districts are “swing” districts for an upcoming election on a contentious political issue. A survey will be conducted in which voters will be asked to rate their opinion regarding
Police are tested for their ability to correctly recognize and identify a suspect based on a witness or victim’s verbal description of the suspect. Scores on the identification test range from 0
Consider the data set(a) Find the range.(b) Use the defining formula to compute the sample standard deviation s.(c) Use the defining formula to compute the population standard deviation (?
Each of the following data sets has a mean of x̅ = 10.(i) 8 9 10 11 12(ii) 7 9 10 11 13(ii) 7 8 10 12 13(a) Without doing any computations, order the data sets according to increasing value of
A Harris Poll indicated that of those adults who drive and have a cell phone, the probability that a driver between the ages of 18 and 24 sends or reads text messages is 0.51. Can this probability be
According to a recent Harris Poll of adults with pets, the probability that the pet owner cooks especially for the pet either frequently or occasionally is 0.24.(a) From this information, can we
M&M plain candies come in various colors. The distribution of colors for plain M&M candies in a custom bag isSuppose you have a large custom bag of plain M&M candies and you choose one candy at
This problem continues the Focus Problem. The solution involves applying several basic probability rules and a little algebra to solve an equation.(a) If the polygraph of Problem 27 indicated that
Given P (A) = 0.3 and P (B) = 0.4:(a) If A and B are mutually exclusive events, compute P (A or B).(b) If P (A and B) 5 0.1, compute P (A or B).
Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be
At Litcheld College of Nursing, 85% of incoming freshmen nursing students are female and 15% are male. Recent records indicate that 70% of the entering female students will graduate with a BSN
The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a
The Eastmore Program is a special program to help alcoholics. In the Eastmore Program, an alcoholic lives at home but undergoes a two-phase treatment plan. Phase I is an intensive group-therapy
The Reverend Thomas Bayes (1702–1761) was an English mathematician who discovered an important rule of probability (see Bayes’s theorem, Appendix I, part I). A key feature of Bayes’s theorem is
Given P (A) = 0.2, P (B) = 0.5, P (A | B) = 0.3:(a) Compute P (A and B).(b) Compute P (A or B)?
Given P (Ac) = 0.8, P (B) = 0.3,P (B | A) = 0.2:(a) Compute P (A and B).(b) Compute P (A or B)?
Lisa is making up questions for a small quiz on probability. She assigns these probabilities: P (A) = 0.3, P (B) = 0.3, P (A and B) = 0.4. What is wrong with these probability assignments?
Barbara is a research biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. She has four
There are five multiple-choice questions on an exam, each with four possible answers. Determine the number of possible answer sequences for the five questions. Only one of the sets can contain
Norb and Gary are entered in a local golf tournament. Both have played the local course many times. Their scores are random variables with the following means and standard deviations.Norb, x1: m1 =
A computer repair shop has two work centers. The first center examines the computer to see what is wrong, and the second center repairs the computer. Let x1 and x2 be random variables representing
Insurance companies know the risk of insurance is greatly reduced if the company insures not just one person, but many people. How does this work? Let x be a random variable representing the
This problem shows you how to make a better blend of almost anything.Let x1, x2, … xn be independent random variables with respective variances σ21, σ22 , … , σ2n.Let c1, c2, ………., cn be
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