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statistics principles and methods

Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions

=+15.20 ● Some investigators think that the concentration(mg/mL) of a particular antigen in supernatant fluids could be related to onset of meningitis in infants. The accompanying data are typical of that given in plots in the article“Type-Specific Capsular Antigen Is Associated with
=+15.19 ● The Gunning Fog index is a measure of reading difficulty based on the average number of words per sentence and the percentage of words with three or more syllables. High values of the Gunning Fog index are associated with difficult reading levels. Independent random samples of six
=+In addition, SSE 5 459.04. Carry out a hypothesis test to determine if there is sufficient evidence to conclude that the mean importance rating of speed is not the same for owners of these three types of cars.
=+attributes that might affect purchase decisions, including comfort, safety, styling, durability, and reliability (“Measuring Values Can Sharpen Segmentation in the Luxury Car Market,” Journal of Advertising Research [1995]: 9–22). Here is summary information on the level of importance of
=+15.18 An investigation carried out to study purchasers of luxury automobiles reported data on a number of different
=+606–621). In addition, F 5 2.56. Construct an ANOVA table, and then state and test the appropriate hypotheses using a .01 significance level.Sample Sample Status Size Mean Continuous smoker 96 2.15 Recent ex-smoker 34 2.21 Long-term ex-smoker 86 1.47 Never smoked 206 1.69
=+15.17 Research carried out to investigate the relationship between smoking status of workers and short-term absenteeism rate (hr/mo) yielded the accompanying summary information (“Work-Related Consequences of Smoking Cessation,” Academy of Management Journal [1989]:
=+21 individuals in the depressive group, 32 individuals in the functional “other” group, and 21 individuals in the brain-damaged group. Complete the ANOVA table. Carry out the appropriate test of hypothesis (use a 5 .01), and interpret your results.Source of Sum of Mean Variation df Squares
=+15.16 The partially completed ANOVA table given in this problem is taken from the article “Perception of Spatial Incongruity” (Journal of Nervous and Mental Disease[1961]: 222), in which the abilities of three different groups to identify a perceptual incongruity were assessed and compared.
=+and the number of miles (at a constant speed) until failure was observed. A partially completed ANOVA table is given. Fill in the missing entries, and test the relevant hypotheses using a .05 level of significance.Source of Sum of Mean Variation df Squares Square F Treatments Error 235,419.04
=+15.15 In an experiment to investigate the performance of four different brands of spark plugs intended for use on a 125-cc motorcycle, five plugs of each brand were tested,
=+b. Is there sufficient evidence to conclude that the mean calcium content is not the same for the four different storage times? Use the value of F from the ANOVA table to test the appropriate hypotheses at significance level .05.
=+a. Verify that the sums of squares and df’s are as given in the ANOVA table.
=+Model 3 32.13815000 10.71271667 6.51 0.0030 Error 20 32.90103333 1.64505167 Corrected Total 23 65.03918333 R-Square C.V. Root MSE CALCIUM Mean 0.494135 2.180018 1.282596 58.8341667
=+Stored Products Research [1992]: 147–151). Four different storage times were considered. Partial output from the SAS computer package is also shown.Storage Period Observations 0 months 58.75 57.94 58.91 56.85 55.21 57.30 1 month 58.87 56.43 56.51 57.67 59.75 58.48 2 months 59.13 60.38 58.01
=+15.14 ● The accompanying data on calcium content of wheat are consistent with summary quantities that appeared in the article “Mineral Contents of Cereal Grains as Affected by Storage and Insect Infestation” (Journal of
=+15.13 An investigation carried out to study the toxic effects of mercury was described in the article “Comparative Responses of the Action of Different Mercury Compounds on Barley” (International Journal of Environmental Studies [1983]: 323–327). Ten different concentrations of mercury
=+b. The actual number of subjects on which each technique was used was 45. After studying the F table, explain why the conclusion in Part (a) still holds.
=+a. Suppose that a total of 33 subjects were used, with each technique applied to 11 of them. Use this information to conduct a level .05 test of the null hypothesis of no difference in mean satisfaction level for the three interview techniques.
=+allowed the employee being evaluated to discuss previous evaluations, the second involved setting goals for the employee, and the third did not allow either feedback or goal setting. After the interviews were concluded, the evaluated employee was asked to indicate how satisfied he or she was
=+15.12 The article “Utilizing Feedback and Goal Setting to Increase Performance Skills of Managers” (Academy of Management Journal [1979]: 516–526) reported the results of an experiment to compare three different interviewing techniques for employee evaluations. One method
=+sports). The following information on scores from the Hopkins Verbal Learning Test (which measures immediate memory recall) was Soccer Nonsoccer Group Athletes Athletes Control Sample size 86 95 53 Sample mean score 29.90 30.94 29.32 Sample standard deviation 3.73 5.14 3.78 In addition, Suppose
=+15.11 In the introduction to this chapter, we considered a study comparing three groups of college students (soccer athletes, nonsoccer athletes, and a control group consisting of students who did not participate in intercollegiate
=+15.10 It has been reported that varying work schedules can lead to a variety of health problems for workers. The article “Nutrient Intake in Day Workers and Shift Workers” (Work and Stress [1994]: 332–342) reported on blood glucose levels (mmol/L) for day-shift workers and workers on two
=+Suppose that the sample sizes were 5, 5, 4, and 6, respectively, and also that MSE 5 .0130. Do the data suggest that true average chlorophyll concentration depends on the variety? State and test the appropriate hypotheses using a significance level of .05.
=+crop. The article “Leaf Gas Exchange and Tuber Yield in Jerusalem Artichoke Cultivars” (Field Crops Research[1991]: 241–252) reported on various plant characteristics.Consider the accompanying data on chlorophyll concentration (gm/m2) for four varieties of Jerusalem artichoke:Variety BI RO
=+15.9 ▼ High productivity and carbohydrate storage ability of the Jerusalem artichoke make it a promising agricultural
=+c. What is the value of MSE?
=+b. The test statistic value is F 5 6.62. Use a test with significance level .05 to decide whether it is plausible that true average satisfaction levels are identical for the three groups.
=+a. What are numerator and denominator df’s for the F test?
=+15.8 The article “An Analysis of Job Sharing, Full-Time, and Part-Time Arrangements” (American Business Review[1989]: 34–40) reported on a study of hospital employees from three different groups. Each employee reported a level of satisfaction with his or her work schedule (1 5 very
=+b. Carry out an ANOVA to determine whether there is evidence to support the claim that the mean price per acre for vineyard land in Sonoma County was not the same for the three years considered. Use a significance level of .05 for your test.
=+a. Construct boxplots for each of the three years on a common axis, and label each by year. Comment on the similarities and differences.
=+15.7 ● Suppose that a random sample of size n 5 5 was selected from the vineyard properties for sale in Sonoma County, California, in each of three years. The following data are consistent with summary information on price per acre (in dollars, rounded to the nearest thousand) for
=+much larger, but for the purposes of this exercise, we use n1 5 n2 5 n3 5 n4 5 20):Number of Times Driving Over 80 mph by Musical Preference MainAcoustic/ stream Hard Heavy Pop Rock Rock Metal 2 3 3 4 3 2 4 3 4 1 3 4 1 2 1 3 3 3 2 3 3 4 1 3 3 3 4 3 3 2 2 3 2 4 2 2 2 4 2 4 1 4 3 4 3 4 3 5 2 2 4 4
=+(3) hard rock, and (4) heavy metal. Each student in these samples was asked how many times he or she had engaged in various reckless activities during the last year. The following table lists data and summary quantities on driving over 80 mph that is consistent with summary quantities given in
=+higher rates of reckless behaviors, such as speeding, drug use, shoplifting, and unprotected sex. Independently chosen random samples were selected from each of four groups of students with different musical preferences at a large high school: (1) acoustic/pop, (2) mainstream rock,
=+15.6 ● The article “The Soundtrack of Recklessness: Musical Preferences and Reckless Behavior Among Adolescents” (Journal of Adolescent Research [1992]: 313–331)described a study whose purpose was to determine whether adolescents who preferred certain types of music reported
=+page 676 resulted from a single-factor experiment involving k 5 4 types of boxes (the sample means and standard deviations are in close agreement with values given in the paper). Do these data provide evidence to support the claim that the mean compression strength is not the same for all four
=+15.5 ● The article “Compression of Single-Wall Corrugated Shipping Containers Using Fixed and Floating Text Platens” (Journal of Testing and Evaluation [1992]:318–320) described an experiment in which several different types of boxes were compared with respect to compression strength
=+Change in Body Fat Mass (kg)Treatment P 1 P P 1 S G 1 P G 1 S 0.6 20.1 21.8 23.3 0.4 23.1 22.9 25.7 21.3 0.3 22.9 24.5 20.2 20.5 22.9 24.3 0.7 20.8 23.7 24.0 20.7 24.2 20.9 24.7 22.0 20.6 n 17 21 17 19 0.100 20.933 23.112 24.605 s 1.139 1.443 1.178 1.122 s2 1.297 2.082 1.388 1.259 Also, N 5 74,
=+with summary quantities given in the article Change in Body Fat Mass (kg)Treatment P 1 P P 1 S G 1 P G 1 S 0.3 23.7 23.8 25.0 0.4 21.0 23.2 25.0 21.7 0.2 24.9 23.0 20.5 22.3 25.2 22.6 22.1 1.5 22.2 26.2 1.3 21.4 23.5 27.0 0.8 1.2 24.4 24.5 1.5 22.5 20.8 24.2 21.2 23.3 21.8 25.2 20.2 0.2 24.0 26.2
=+15.4 ● The experiment described in Example 15.4 also gave data on change in body fat mass for men (“Growth Hormone and Sex Steroid Administration in Healthy Aged Women and Men,” Journal of the American Medical Association [2002]: 2282–2292). Each of 74 male subjects who were over age 65
=+c. Answer the question posed in Part (b) if the F value given there resulted from sample sizes n1 5 9, n2 5 8, n3 5 7, and n4 5 8.
=+b. If each sample consisted of eight individuals and the value of the ANOVA F statistic was F 5 4.37, what conclusion would be appropriate for a test with a 5 .01?
=+a. What hypotheses would you test to decide whether average length of stay was related to health plan? (Note:Carefully define the population characteristics of interest.)
=+15.3 Employees of a certain state university system can choose from among four different health plans. Each plan differs somewhat from the others in terms of hospitalization coverage. Four samples of recently hospitalized individuals were selected, each sample consisting of people covered by a
=+15.2 Give as much information as you can about the P-value of the single-factor ANOVA F test in each of the following situations.a. k 5 5, n1 5 n2 5 n3 5 n4 5 n5 5 4, F 5 5.37b. k 5 5, n1 5 n2 5 n3 5 5, n4 5 n5 5 4, F 5 2.83c. k 5 3, n1 5 4, n2 5 5, n3 5 6, F 5 5.02d. k 5 3, n1 5 n2 5 4, n3 5 6,
=+15.1 Give as much information as you can about the P-value for an upper-tailed F test in each of the following situations.a. df1 5 4, df2 5 15, F 5 5.37b. df1 5 4, df2 5 15, F 5 1.90c. df1 5 4, df2 5 15, F 5 4.89d. df1 5 3, df2 5 20, F 5 14.48e. df1 5 3, df2 5 20, F 5 2.69f. df1 5 4, df2 5 50, F
=+e. Do you think there were many scores below 40? Explain.
=+Use the methods developed in this chapter to summarize the data; include an interpretation or discussion wherever appropriate. (Note: The author of the paper used a rather sophisticated statistical analysis to conclude that people cannot walk in a straight line and suggested several explanations
=+Rather than weighing passengers, airlines currently use estimates of average passenger and luggage weights.After the 2003 accident, this estimate was increased by 10 lbs. for passengers and 5 lbs. for luggage. Although an airplane can fly if it is somewhat overweight if all systems are working
=+The article “Airlines Should Weigh Passengers, Bags, NTSB Says” (USA Today , February 27, 2004) states that the National Transportation Safety Board recommended that airlines weigh passengers and their bags to prevent overloaded planes from attempting to take off. This recommendation was the
=+4. Write a short article for your school paper summarizing your findings regarding student behavior. Your article should include both numerical and graphical summaries.
=+3. Summarize the resulting data using both numerical and graphical summaries. Be sure to address both center and variability.
=+2. Use the plan developed in Activity 2.1 to collect data on the variable you have chosen for your study.
=+1. With your group, pick one of the following activities to be the focus of your study:i. Surfing the web ii. Studying or doing homework iii. Watching TV iv. Exercising v. Sleeping or you may choose a different activity, subject to the approval of your instructor.
=+In this activity, you will work in groups to collect data that will provide information about how many hours per week, on average, students at your school spend engaged in a particular activity. You will use the sampling plan designed in Activity 2.1 to collect the data.
=+If your reaction time is 4.2 sec for the first stimulus and 1.8 sec for the second stimulus, to which stimulus are you reacting (compared to other individuals) relatively more quickly?
=+4.50 The accompanying table gives the mean and standard deviation of reaction times (in seconds) for each of two different stimuli:Stimulus Stimulus 1 2 Mean 6.0 3.6 Standard deviation 1.2 0.8
=+8.01a. Summarize this data set with a frequency distribution.Construct the corresponding histogram.b. Use the histogram in Part (a) to find approximate values of the following percentiles:i. 50th iv. 90th ii. 70th v. 40th iii. 10th
=+4.49 ● ▼ The following data values are 1989 per capita expenditures on public libraries for each of the 50 states:29.48 24.45 23.64 23.34 22.10 21.16 19.83 18.01 17.95 17.23 16.53 16.29 15.89 15.85 13.64 13.37 13.16 13.09 12.66 12.37 11.93 10.99 10.55 10.24 10.06 9.84 9.65 8.94 7.70 7.56 7.46
=+4.48 The average reading speed of students completing a speed-reading course is 450 words per minute (wpm). If the standard deviation is 70 wpm, find the z score associated with each of the following reading speeds.a. 320 wpmc. 420 wpmb. 475 wpmd. 610 wpm
=+distribution of the variable number of answers changed from right to wrong? What can you say about the number of students who changed at least six answers from correct to incorrect?
=+4.47 The paper “Answer Changing on Multiple-Choice Tests” (Journal of Experimental Education [1980]: 18–21)reported that for a group of 162 college students, the average number of responses changed from the correct answer to an incorrect answer on a test containing 80 multiplechoice items
=+4.46 Suppose that your statistics professor returned your first midterm exam with only a z score written on it. She also told you that a histogram of the scores was approximately normal. How would you interpret each of the following z scores?a. 2.2d. 1.0b. 0.4e. 0c. 1.8
=+be said about the proportion of the time that the scale actually showed a weight that was within 0.25 oz of the true value of 50 oz? (Hint: Use Chebyshev’s Rule.)
=+4.45 An advertisement for the “30-in. Wonder” that appeared in the September 1983 issue of the journal Packaging claimed that the 30-in. Wonder weighs cases and bags up to 110 lb and provides accuracy to within 0.25 oz. Suppose that a 50-oz weight was repeatedly weighed on this scale and
=+b. Compute (approximately) the following percentiles:i. 86th iv. 95th ii. 15th v. 10th iii. 90th
=+a. Construct the corresponding histogram.
=+4.44 The paper “Modeling and Measurements of Bus Service Reliability” (Transportation Research [1978]: 253–256) studied various aspects of bus service and presented data on travel times from several different routes. The accompanying frequency distribution is for bus travel times from
=+d. Why would you not use Chebyshev’s Rule to answer the questions posed in Parts (a)–(c)?
=+c. What can be said about the approximate percentage of observations between 2000 and 2500?
=+b. Approximately what percentage of sample observations are outside the interval from 2000 to 4000?
=+4.43 A sample of concrete specimens of a certain type is selected, and the compressive strength of each specimen is determined. The mean and standard deviation are calculated as 5 3000 and s 5 500, and the sample histogram is found to be well approximated by a normal curve.a. Approximately what
=+4.42 Suppose that your younger sister is applying for entrance to college and has taken the SATs. She scored at the 83rd percentile on the verbal section of the test and at the 94th percentile on the math section of the test. Because you have been studying statistics, she asks you for an
=+4.41 A student took two national aptitude tests. The national average and standard deviation were 475 and 100, respectively, for the first test and 30 and 8, respectively, for the second test. The student scored 625 on the first test and 45 on the second test. Use z scores to determine on which
=+4.40 The article “Taxable Wealth and Alcoholic Beverage Consumption in the United States” (Psychological Reports[1994]: 813–814) reported that the mean annual adult consumption of wine was 3.15 gal and that the standard deviation was 6.09 gal. Would you use the Empirical Rule to
=+c. In a sample of non–Los Angeles mobile homes, the average kitchen NO2 concentration during the winter was 24.76 ppb, and the standard deviation was 17.20. Do these values suggest that the histogram of sample observations did not closely resemble a normal curve? (Hint: What is)
=+b. Inside what interval is it guaranteed that at least 89%of the concentration observations will lie?
=+11.34. Making no assumptions about the shape of the NO2 distribution, what can be said about the percentage of observations between 14.24 and 59.60?
=+a. In one sample of mobile homes in the Los Angeles area, the mean NO2 concentration in kitchens during the summer was 36.92 ppb, and the standard deviation was
=+f. How well do the statements in Part (e) based on Chebyshev’s Rule agree with the actual percentages for the travel time distribution? (Hint: You can estimate the actual percentages from the given relative frequency distribution.)4.39 Mobile homes are tightly constructed for energy
=+ii. the percentage of travel times that were between 0 and 47 min
=+e. Use the mean and standard deviation given in Part (d)and Chebyshev’s Rule to make a statement about i. the percentage of travel times that were between 0 and 75 min
=+d. The approximate mean and standard deviation for the travel time distribution are 27 min and 24 min, respectively. Based on this mean and standard deviation and the fact that travel time cannot be negative, explain why the travel time distribution could not be well approximated by a normal
=+c. Based on the histogram from Part (a), would it be appropriate to use the Empirical Rule to make statements about the travel time distribution? Explain why or why not.
=+b. Describe the interesting features of the histogram from Part (a), including center, shape, and spread.
=+a. Draw the histogram for the travel time distribution. In constructing the histogram, assume that the last interval in the relative frequency distribution (90 or more) ends at 200; so the last interval is 90 to ,200. Be sure to use the density scale to determine the heights of the bars in the
=+4.38 The U.S. Census Bureau (2000 census) reported the following relative frequency distribution for travel time to work for a large sample of adults who did not work at home:Travel Time Relative(minutes) Frequency 0 to ,5 .04 5 to ,10 .13 10 to ,15 .16 15 to ,20 .17 20 to ,25 .14 25 to ,30 .05
=+b. Roughly what proportion of vehicle speeds exceeded 57 mph?
=+4.37 ▼ In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5000 accidents, the average speed was 42 mph and that the standard deviation was hat the
=+d. Assuming that the distribution of times is normal, approximately what percentage of times are between 25 and 45 min? less than 20 min or greater than 50 min? less than 20 min?
=+c. Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 20 min or greater than 50 min?
=+b. Without assuming anything about the distribution of times, at least what percentage of the times are between 25 and 45 min?
=+2 standard deviations away from the mean?
=+1 standard deviation below the mean? What values are
=+c. Construct a comparative boxplot, and use it as a basis for comparing and contrasting the two samples.4.36 collea. W
=+b. Are there any outliers in either sample? Any extreme outliers?
=+a. Determine the median, quartiles, and interquartile range for each of the two samples.

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