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essentials of statistics

Questions and Answers of Essentials Of Statistics

13. Mulvihill, Obuseh, and Caldwell (2008) conducted a survey evaluating healthcare providers’ perception of a new state children’s insurance program. One question asked the providers whether
12. In Problem 11, a researcher asked college students to evaluate three new cell phone designs. However, the researcher suspects that college students may have criteria that are different from those
11. A communications company has developed three new designs for a cell phone. To evaluate consumer response, a sample of 120 college students is selected and each student is given all three phones
10. The color red is often associated with anger and male dominance. Based on this observation, Hill and Barton(2005) monitored the outcome of four combat sports(boxing, tae kwan do, Greco-Roman
9. Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that the younger drivers are much more likely to
8. A professor in the psychology department would like to determine whether there has been a significant change in grading practices over the years. It is known that the overall grade distribution
7. Suppose that the researcher from the previous problem repeated the study of married couples’ initials using twice as many participants and obtaining observed frequencies that exactly double the
6. Research has demonstrated that people tend to be attracted to others who are similar to themselves. One studey demonstrated that individuals are disproportionately more likely to marry those with
5. To investigate the phenomenon of “home-team advantage,” a researcher recorded the outcomes from 64 college football games on one Saturday in October.Of the 64 games, 42 were won by home teams.
4. Data from the Motor Vehicle Department indicate that 80% of all licensed drivers are older than age 25.a. In a sample of n 60 people who recently received speeding tickets, 38 were older than 25
3. A developmental psychologist would like to determine whether infants display any color preferences. A stimulus consisting of four color patches (red, green, blue, and yellow) is projected onto the
2. The student population at the state college consists of 55% females and 45% males.a. The college theater department recently staged a production of a modern musical. A researcher recorded the
1. Parametric tests (such as t or ANOVA) differ from nonparametric tests (such as chi-square) primarily in terms of the assumptions they require and the data they use. Explain these differences.
26. A set of n 15 pairs of X and Y values has a correlation of r +.80 with SSY 75, and the regression equation for predicting Y is computed.a. Find the standard error of estimate for the regression
25. Problem 9 described a study examining the effectiveness of a 7-Minute Screen test for Alzheimer’s disease. The study evaluated the relationship between scores from the 7-Minute Screen and
24.a. Briefly explain what is measured by the standard error of estimate.b. How is the magnitude of the standard error of estimate related to the correlation?
23. For the following scores, X Y 3 0 8 10 7 8 5 3 7 7 6 8a. Find the regression equation for predicting Y from X.b. Calculate the predicted Y value for each X.
22. For the following data:a. Find the regression equation for predicting Y from X.b. Use the regression equation to find a predicted Y for each X.c. Find the difference between the actual Y value
21. A set of n 25 pairs of scores (X and Y values) produce a regression equation of ˆY 2X 7. Find the predicted Y value for each of the following X scores:0, 1, 3, 2.
20. A set of n 20 pairs of scores (X and Y values) has SSX 25, SSY 16, and SP 12.5. If the mean for the X values is M 6 and the mean for the Y values is M 4.a. Calculate the Pearson correlation for
19. The regression equation is intended to be the “bestfitting” straight line for a set of data. What is the criterion for “best fitting”?
17. A researcher measures three variables, X, Y, and Z for each individual in a sample of n 25. The Pearson correlations for this sample are rXY 0.8, rXZ 0.6, and rYZ 0.7.a. Find the partial
16. A researcher would like to evaluate the relationship between a person’s age and his or her preference between two leading brands of cola. In a sample of 12 people, the researcher found that 5
15. Problem 23 in Chapter 10 presented hypothetical data showing that elderly people who own dogs are significantly less likely to pay visits to their doctors than those who do not own pets. The
14. It appears that there is a significant relationship between cognitive ability and social rank, at least for birds. Boogert, Reader, and Laland (2006) measured social rank and individual learning
13. A common concern for students (and teachers) is the assignment of grades for essays or term papers.Because there are no absolute right or wrong answers, these grades must be based on a judgment
12. As a student, you probably have noticed a curious phenomenon. In every class, there are some students who zip through exams and turn in their papers while everyone else is still on page 1. Other
11. As we have noted in previous chapters, even a very small effect can be significant if the sample is large enough. For each of the following, determine how large a sample is necessary for the
10. Assuming a two-tailed test with .05, how large a correlation is needed to be statistically significant for each of the following samples?a. A sample of n 10b. A sample of n 20c. A sample of n 30
9. Identifying individuals with a high risk of Alzheimer’s disease usually involves a long series of cognitive tests. However, researchers have developed a 7-Minute Screen, which is a quick and
8. Correlation studies are often used to help determine whether certain characteristics are controlled more by genetic influences or by environmental influences.These studies often examine adopted
7. For the following set of scores, X Y 3 8 8 1 5 6 6 3 6 6 8 6a. Compute the Pearson correlation.b. Add 2 points to each X value and compute the correlation for the modified scores. How does adding
6. For the following scores, X Y 3 12 6 7 3 9 5 7 3 10
5. For the following scores,a. Sketch a scatter plot showing the six data points.b. Just looking at the scatter plot, estimate the value of the Pearson correlation.c. Compute the Pearson correlation.
4. Calculate SP (the sum of products of deviations) for the following scores. Note: Both means are decimal values, so the computational formula works well:X Y 1 4 4 3 5 9 0 2 X Y 2 4 6 3 1 8 3 5
3. Calculate SP (the sum of products of deviations) for the following scores. Note: Both means are whole numbers, so the definitional formula works well:
2. What information is provided by the numerical value of the Pearson correlation?
1. What information is provided by the sign ( or ) of the Pearson correlation?
4. A recent study of driving behavior suggests that self-reported measures of high driving skills and low ratings of safety skills create a dangerous combination(Sümer, Özkan, & Lajunen, 2006).
3. Briefly describe what is meant by an interaction between factors in a two-factor research study.
2. Loss of hearing can be a significant problem for older adults. Although hearing aids can correct the physical problem, people who have lived with hearing impairment often develop poor
1. Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts, &Brown, 2005). Based on pre-treatment
25. Mathematics word problems can be particularly difficult, especially for primary-grade children. A recent study investigated a combination of techniques for teaching students to master these
24. The following data are from a two-factor study examining the effects of three treatment conditions on males and females.a. Use an ANOVA with.05 for all tests to evaluate the significance of the
23. The following table summarizes the results from a two-factor study with 3 levels of factor A and 3 levels of factor B using a separate sample of n 9 participants in each treatment condition. Fill
22. The following table summarizes the results from a two-factor study with 2 levels of factor A and 3 levels of factor B using a separate sample of n 8 participants in each treatment condition. Fill
21. Most sports injuries are immediate and obvious, like a broken leg. However, some can be more subtle, like the neurological damage that may occur when soccer players repeatedly head a soccer ball.
20. A researcher conducts an independent-measures, two-factor study with two levels of factor A and four levels of factor B, using a separate sample of n 10 participants in each treatment
19. The following matrix presents the results from an independent-measures, two-factor study with a sample of n 10 participants in each treatment condition.Note that one treatment mean is
18. For the data in the following matrix:No Treatment Treatment Male M 5 M 3 Overall M 4 Female M 9 M 13 Overall M 11 overall M 7 overall M 8a. Describe the mean difference that is the main effect
17. Briefly explain what happens during the second stage of the two-factor ANOVA.
16. The structure of a two-factor study can be presented as a matrix with the levels of one factor determining the rows and the levels of the second factor determining the columns. With this
15. Define each of the following terms:a. Factorb. Levelc. Two-factor study
14. A repeated-measures experiment comparing only two treatments can be evaluated with either a t statistic or an ANOVA. As we found with the independentmeasures design, the t test and the ANOVA
13. A recent study indicates that simply giving college students a pedometer can result in increased walking(Jackson & Howton, 2008). Students were given pedometers for a 12-week period, and asked to
12. The following summary table presents the results from a repeated-measures ANOVA comparing four treatment conditions, each with a sample of n 10 subjects. Fill in the missing values in the
11. A researcher is evaluating the effectiveness of a speed-reading course. A standardized reading test, measuring both speed and comprehension, was given to a sample of n 15 students before the
10. The following data are from an experiment comparing three different treatment conditions:ABC 012 N 15 255 X2 354 126 549 288 T 10 T 20 T 30 SS 14 SS 30 SS 30a. If the experiment uses an
9. The following data were obtained from a repeatedmeasures study comparing three treatment conditions.a. Use a repeated-measures ANOVA with.05 to determine whether there are significant mean
8. The following data were obtained from a repeatedmeasures study comparing two treatment conditions.Use a repeated-measures ANOVA with.05 to determine whether there are significant mean differences
7. The following data were obtained from a repeatedmeasures study comparing three treatment conditions.Use a repeated-measures ANOVA with.05 to determine whether there are significant mean
6. A published report of a repeated-measures research study includes the following description of the statistical analysis. “The results show significant differences among the treatment conditions,
5. A researcher uses a repeated-measures ANOVA to evaluate the results from a research study and reports an F-ratio with df 3, 36.a. How many treatment conditions were compared in the study?b. How
4. A researcher conducts a repeated-measures experiment using a sample of n 10 subjects to evaluate the differences among three treatment conditions. If the results are examined with an ANOVA, what
3. A researcher conducts an experiment comparing three treatment conditions. The data consist of n 20 scores for each treatment condition.a. If the researcher used an independent-measures design,
2. The repeated-measures ANOVA can be viewed as a two-stage process. What is the purpose for the second stage?
1. How does the denominator of the F-ratio (the error term) differ for a repeated-measures ANOVA compared to an independent-measures ANOVA?
22. First-born children tend to develop language skills faster than their younger siblings. One possible explanation for this phenomenon is that first-borns have undivided attention from their
21. One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds with small brains, relative to their body
20. The following data represent the results from an independent-measures study comparing two treatment conditions.a. Use an independent-measures t test with .05 to determine whether there is a
19. The following values summarize the results from an independent-measures study comparing two treatment conditions.a. Use an independent-measures t test with .05 to determine whether there is a
18. The following data were obtained from an independentmeasures research study comparing three treatment conditions. Use an ANOVA with .05 to determine whether there are any significant mean
17. A developmental psychologist is examining the development of language skills from age 2 to age 5.Four different groups of children are obtained, one for each age, with n 15 children in each
16. A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n 10 in each sample. The first sample receives the drug
15. The following summary table presents the results from an ANOVA comparing three treatment conditions with n 12 participants in each condition. Complete all missing values. (Hint: Start with the df
14. There is some evidence that high school students justify cheating in class on the basis of poor teacher skills or low levels of teacher caring (Murdock, Miller, and Kohlhardt, 2004). Students
13. A research report from an independent-measures study states that there are significant differences between treatments, F(2, 54) 3.58, p < .05.a. How many treatment conditions were compared in the
12. A researcher reports an F-ratio with df 3, 36 from an independent-measures research study.a. How many treatment conditions were compared in the study?b. What was the total number of participants
11. Binge drinking on college campuses has been a hot topic in the popular media and in scholarly research. Flett, Goldstein, Wall, Hewitt, Wekerle, and Azzi (2008) report the results of a study
10. For the preceding problem you should find that there are significant differences among the three treatments. One reason for the significance is that the sample variances are relatively small. To
9. The following data summarize the results from an independent-measures study comparing three treatment conditions.I II III n 5 n 5 n 5 M 2 M 5 M 8 N 15 T 10 T 25 T 40 G 75 SS 16 SS 20 SS 24 ΣX2
8. For the preceding problem you should find that there are significant differences among the three treatments. The primary reason for the significance is that the mean for treatment I is
7. The following data summarize the results from an independent-measures study comparing three treatment conditions.I II III n 6 n 6 n 6 M 1 M 5 M 6 N 18 T 6 T 30 T 36 G 72 SS 30 SS 35 SS 40 ΣX2
6. The following data represent the results from an independent-measures study comparing three treatments.a. Compute SS for the set of 3 treatment means.(Use the three means as a set of n 3 scores
5. Posttests are done after an ANOVA.a. What is the purpose of posttests?b. Explain why you would not do posttests if the analysis is comparing only two treatments.c. Explain why you would not do
4. Explain why you should use ANOVA instead of several t tests to evaluate mean differences when an experiment consists of three or more treatment conditions.
3. Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-ratio, and indicate whether the size of
2. Describe the similarities between an F-ratio and a t statistic.
1. Explain why the expected value for an F-ratio is 1.00 when the null hypothesis is true.
21. In Chapter 11, problem 22 presented data comparing the accuracy of Olympic marksmen for shots fired during heartbeat compared to shots fired between heartbeat. The data are presented again
20. Problem 16 in Chapter 11 described a study examining the effect of eating oatmeal regularly on cholesterol.Cholesterol was measured before and after adding oatmeal to the diet of a sample of n 9
19. A research study has demonstrated that self-hypnosis can be an effective treatment for allergies (Langewitz, Izakovic, & Wyler, 2005). The researchers recruited a sample of patients with moderate
18. A researcher would like to determine how physical endurance is affected by a common herbal supplement.The researcher measures endurance for a sample of n 9 participants. Each individual is then
17. The stimulant Ritalin has been shown to increase attention span and improve academic performance in?children with ADHD (Evans, et al., 2001). To demonstrate the effectiveness of the drug, a
16. Problem 23 in Chapter 10 described a study demonstrating that elderly people who own dogs are less likely to pay visits to their doctors than are those who do not own pets. The data are presented
15. Problem 18 in Chapter 10 reported a research study in which eyewitness reports of an automobile accident were influenced by the language used to ask questions (Loftus& Palmer, 1974). One group of
14. Hallam, Price, and Katsarou (2002) investigated the influence of background noise on classroom performance for children aged 10 to 12. In one part of the study, calming music led to better
13. Downs and Abwender (2002) evaluated soccer players and swimmers to determine whether the routine blows to the head experienced by soccer players produced long-term neurological deficits. In the
12. Numerous studies have found that males report higher self-esteem than females, especially for adolescents(Kling, Hyde, Showers, & Buswell, 1999). Typical results show a mean self-esteem score of
11. A common test of short-term memory requires participants to repeat a random string of digits that was presented a few seconds earlier. The number of digits is increased on each trial until the

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