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modern mathematical statistics with applications

Modern Mathematical Statistics With Applications 3rd Edition Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton - Solutions

A study at Bentley College, a large business school in the eastern United States, examined students’ anxiety levels toward the subject of accounting (“Determinants of Accounting Anxiety in Business Students,” J. College Teach. Learn. 2004). A representative sample of 1020 students completed
The article “Iron and Manganese Present in Underground Water Promote Biochemical, Genotoxic, and Behavioral Alterations in Zebrafish” (Environ. Sci. Pollut. Res. 2019: 23555–23570) reports the following data on micronucleus frequency in the muscle tissues for zebrafish exposed to varying
Consider the data on maximum load for cracked wood beams presented in Exercise 4. Would it make sense to apply Tukey’s method to this data? Why or why not?Data From Exercise 4The article “Load-Carrying Capacity of Lengthwise Cracked Wood Beams Retrofitted by Self-Tapping Screws” (J. Struct.
Does music affect memorization skills, and does it matter if the music includes vocals/ lyrics? In one experiment (P. Ramos, “The Impact of Music on Short Term Memory and Cognitive Processes,” Univ. of Bridgeport, 2017), subjects were randomly assigned to one of four environments: (A) an
One popular approach to lower back pain is to apply a piece of durable tape along the lower spine. In one study, 108 women with lower back pain were randomly assigned to receive one of four treatments: Kinesio tape applied to a tense back (KTT), Kinesio tape without any back tension (KTNT),
Plastic waste, particularly microplastics in oceans and waterways, has become an increasing global environmental concern. The article “Environmentally Relevant Concentrations of Microplastic Particles Influence Larval Fish Ecology” (Science, 3 June 2016: 1213–1216) describes an experiment in
The article “Differences in Impact Performance of Bicycle Helmets During Oblique Impacts” (J. Biomech. Engr. 2018) describes an experiment in which 10 different bicycle helmet brands (4 of each brand, for 40 total helmets) were strapped onto a mannequin head and subjected to a frontal impact at
The article “Load-Carrying Capacity of Lengthwise Cracked Wood Beams Retrofitted by Self-Tapping Screws” (J. Struct. Engr. 2017) provides data on the maximum load (kN) of J = 5 specimens of I = 4 types of wood beams used in housing: intact beams (L1), long, centered cracks (L2), short, centered
Freezing and thawing out food can adversely affects its texture. In one experiment described in the article “Effects of Freezing Treatments Before Convective Drying on Quality Parameters” (J. of Food Engr. 2019: 15–24), apple pieces were frozen using a –20°C freezer (F20), a –80°C
An experiment to compare I = 5 brands of golf balls involved using a robotic driver to hit J = 7 balls of each brand. The resulting between-sample and within-sample estimates of σ2 were MSTr = 123.50 and MSE = 22.16, respectively.a. State and test the relevant hypotheses using a significance
For the data of Exercise 29 find a 90% confidence interval for the ratio of population standard deviations, and relate your CI to the test of Exercise 74.Data From Exercise 29Data From Exercise 74 As the population ages, there is increasing concern about accident-related injuries to the elderly.
In this exercise, we develop a CI for that is valid whatever the shape of the population distribution as long as it is continuous.Let X1,. . . , Xn be a random sample from the distribution and Y1< . . .< Yn denote the corresponding ordered values (smallest observation, second smallest, and so
Because of extra-inning games, the median might be a more meaningful statistic for the length-of-game data in the previous exercise. The median length of all 2430 MLB games in 2018 was min.a. Use software and the data in the previous exercise to obtain a bootstrap sample of medians.b. Obtain a 95%
Exercise 16 of Chapter 1 presented data on the noise level (dBA) experienced by a sample of 77 individuals working at a particular office.a. Construct a 95% confidence interval for the true average noise level experienced by people working in this office.b. Would it be feasible to construct a valid
If X has the pdf ƒX(x) = x/8, 0 < x < 4, find a transformation Y ∼ g(X) such that Y ∼ Unif[0, 1]. The target is to achieve ƒY(y) = 1 for 0 ≤ y ≤ 1. The Transformation Theorem will allow you to find h(y), from which g(x) can be obtained.Transformation Theorem Let X have pdf fx(x) and
For θ > 0 consider a random sample from a uniform distribution on the interval from θ to 2θ, and use the factorization theorem to determine a sufficient statistic for θ. The Factorization Theorem How can a sufficient statistic be identified? It may seem as though one would have to select a
Assume that the number of alpha particles emitted in one second by a particular radioactive source has a Poisson distribution with parameter μ. Consider estimating μ based on a random sample X1, X2, …, Xn.a. Find the Fisher information in a single observation using both (7.5) and (7.6).Equation
The number of attempts required to successfully transmit a message across a noisy channel can be modeled by a geometric distribution, whose pmf is (1 – p)x–1p for x = 1, 2, 3, …. To estimate the unknown parameter p we obtain the random sample X1, X2, …, Xn from this geometric
Here are the alcohol percentages for a random sample of 16 beers (light beers excluded): a. Construct a normal probability plot of the data. Is it plausible that these values represent a sample from a normal distribution?b. Calculate a 95% CI for the mean alcohol percentage of all nonlight
Here are the lengths (in minutes) of the 63 nine-inning games from the first week of the 2001 major league baseball season:Assume that this is a random sample of nineinning games (the mean differs by 12 s from the mean for the whole season).a. Give a 95% confidence interval for the population
A random sample of 50 patients who had been seen at an outpatient clinic was selected, and the waiting time to see a physician was determined for each one, resulting in a sample mean time of 40.3 min and a sample standard deviation of 28.0 min (suggested by the article “An Example of Good but
The article “Evaluating Tunnel Kiln Performance” (Amer. Ceramic Soc. Bull., Aug. 1997: 59–63) gave the following summary information for fracture strengths (MPa) of n = 169 ceramic bars fired in a particular kiln: x̅ = 89:10; s = 3:73.a. Calculate a (two-sided) confidence interval for
As health care costs rise and health care systems worldwide become overburdened, patients are made to wait longer for critical procedures. One Canadian study of 539 cardiac patients waiting for cardiac bypass surgery found a mean wait time of 19 days with a standard deviation of ten days (“Wait
A sample of 66 obese adults was put on a low-carbohydrate diet for a year. The average weight loss was 11 lb and the standard deviation was 19 lb. Calculate a 99% lower confidence bound for the true average weight loss. What does the bound say about confidence that the mean weight loss is positive?
A study was done on 41 first-year medical students to see if their anxiety levels changed during the first semester. One measure used was the level of serum cortisol, which is associated with stress. For each of the 41 students the level was compared during finals at the end of the semester against
University administrators wish to estimate the mean time to graduation, for the population of students who actually graduate, to within ± 3 months (one-quarter). It is known that the maximum time to graduation is eight years (96 months) and the minimum time is three years (36 months), so that a
Young people may feel they are carrying the weight of the world on their shoulders, when what they are actually carrying too often is an excessively heavy backpack. The article “Effectiveness of a School- Based Backpack Health Promotion Program” (Work 2003: 113–123) reported the following
According to Oklahoma State University’s 2015 Food Demand Survey, 859 of 1044 randomly selected adults support mandatory labels on foods produced with genetic engineering (popularly called GMO products). Construct an approximate 95% confidence interval for the proportion of all adults who support
In a survey of 1100 drivers, 90% admitted to careless or aggressive driving during the previous six months (“Nine out of Ten Drivers Admit in Survey to Having Done Something Dangerous,” Knight Ridder Newspapers, Jul. 8, 2005). Assuming these 1100 drivers may be treated as a random sample of all
A June, 2019 Gallup survey of 1018 randomly selected US adults found that 53% supported the government sponsoring a manned mission to Mars.a. Construct and interpret a 95% lower confidence bound for the proportion of all US adults who support such a mission.b. Does your answer to part (a) clearly
The article “Repeatability and Reproducibility for Pass/Fail Data” (J. Testing Eval. 1997: 151–153) reported that in n = 48 trials in a particular laboratory, 16 resulted in ignition of a particular type of substrate by a lighted cigarette. Let p denote the long-run proportion of all such
The article “Teens and Young Adults Embrace Online Multiplayer and Competitive Video Games” (Washington Post, Apr. 3, 2018) reported that, in a survey of 522 Americans age 14–21, 38% said they consider themselves a fan of competitive gaming. Construct a 99% confidence interval for the
As reported by CNBC (Dec. 11, 2018), 57% of people surveyed admitted to shopping online while at work. The survey was based on a random sample of n = 2020 US adults. Construct and interpret a 90% upper confidence bound for the proportion of all US adults who shop online while at work.
There is increasing concern within the health sciences community over the use of electronic tobacco products. The article “Exposure to Tobacco and Nicotine Product Advertising: Associations with Perceived Prevalence of Use Among College Students” (Amer. J. College Health, Volume 66, 2018, Issue
The article “Broad Agreement on Most Ideas to Curb School Shootings” from the Gallup.com website reported on a survey carried out from March 5–11, 2018. There was overwhelming support for more training of school and security personnel, and for background checks for all gun sales. However,
Here are the names of 12 orchestra conductors and their performance times in minutes for Beethoven’s Ninth Symphony:a. Check to see that normality is a reasonable assumption for the performance time distribution.b. Compute a 95% CI for the population standard deviation, and interpret the
A mortgage company wishes to estimate the proportion of all borrowers who default on their home loans, to within a margin of error of 2 percentage points (±.02). What sample size is required to achieve this at the 90% confidence level? How does the answer change if it is believed initially that
A recent student project asked students at Cal Poly (where one of the authors teaches) whether they have ever been arrested on alcohol- or drug-related charges, including drunk driving. Out of 57 students surveyed in the College of Business, only four reported they had been arrested (the surveys
In a survey, students gave their study time per week (h), and here are the 22 values:A 95% confidence interval for the population mean μ is desired.a. Compute the t-based confidence interval of Section 8.2.b. Create a normal probability plot. Is it apparent that the data set is not normal, so the
Here are 68 weight gains (lb) for pregnant women from conception to delivery (“Classifying Data Displays with an Assessment of Displays Found in Popular Software,” Teach. Statist., Autumn 2002: 96–101). A 95% CI for the population mean weight gain μ is desired.a. Compute the t-based
Nine Australian soldiers were subjected to extreme conditions, which involved a 100- min walk with a 25-lb pack when the temperature was 40°C (104°F). One of them overheated (above 39°C) and was removed from the study. Here are the rectal Celsius temperatures of the other eight at the end of the
Before opening a new location, franchise companies conduct market research to determine if sufficient demand exists for their products. A national sandwich chain recently conducted a survey to investigate opening a franchise in a particular town. Among 300 households contacted through random-digit
There were 12 first-round heats in the men’s 100-m race at the 1996 Atlanta Summer Olympics. Here are the reaction times in seconds (time to first movement) of the top four finishers of each heat. The first 12 are the 12 winners, then the second place finishers, and so on.Because reaction time
Let θ1 and θ2 denote the mean weights for animals of two different species. A biologist wishes to estimate the ratio θ1/θ2. Unfortunately the species are extremely rare, so the estimate will be based on finding a single animal of each species. Let Xi denote the weight of the species i
The industry standard for the amount of alcohol poured into many types of drinks (e.g., gin for a gin and tonic, whiskey on the rocks) is 1.5 oz. Each individual in a sample of 8 bartenders with at least 5 years of experience was asked to pour rum for a rum and coke into a short, wide (tumbler)
Let the test statistic T have a t distribution when H0 is true. Give the significance level for each of the following situations:a.b.c. Ha: > Mo, df = 15, rejection region t> 3.733
Consider 95% CIs for two different parameters θ1 and θ2, and let Ai (i = 1, 2) denote the event that the value of θi is included in the random interval that results interval that results in the CI. Thus P(Ai) = .95.a. Suppose that the data on which the CI for θ1 is based is
The one-sample CI for a normal mean and PI for a single observation from a normal distribution were both based on the central t distribution. A CI for a particular percentile (e.g., the 1st percentile or the 95th percentile) of a normal population distribution is based on the noncentral t
A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows:a. Does this data suggest that the population mean reading under these conditions differs from 100? State and test the appropriate hypotheses using α =
In an experiment designed to measure the time necessary for an inspector’s eyes to become used to the reduced amount of light necessary for penetrant inspection, the sample average time for n = 9 inspectors was 6.32 s and the sample standard deviation was 1.65 s. It has previously been assumed
The target thickness for silicon wafers used in a type of integrated circuit is 245 μm. A sample of 50 wafers is obtained and the thickness of each one is determined, resulting in a sample mean thickness of 246.18 μm and a sample standard deviation of 3.60 μm. Does this data suggest that true
On the label, Pepperidge Farm bagels are said to weigh four ounces each (113 g). A random sample of six bagels resulted in the following weights (in grams):a. Based on this sample, is there any reason to doubt that the population mean is at least 113 g?b. Suppose that the population mean is
The article “Development of Novel Industrial Laminated Planks from Sweetgum Lumber” (J. Bridge Engr. 2008: 64–66) provides the following data on the modulus of rupture (psi) for a sample of planks:a. Perform a hypothesis test at the .01 level to determine if the true modulus of rupture for
Although the U.S. Food and Drug Administration recommends against using kitchen utensils to dose liquid medicines, many people still do so, resulting in dosing errors and even pediatric poisonings. The letter “Spoons Systematically Bias Dosing of Liquid Medicine” (Annals of Internal Med. 2010:
Exercise 46 in Chapter 1 gave n = 26 observations on escape time (sec) for oil workers in a simulated exercise, from which the sample mean and sample standard deviation are 370.69 and 24.36, respectively. Suppose the investigators had believed a priori that true average escape time would be at most
Let F(x, ν, δ) denote the cdf of the noncentral t distribution.a. Determine the power function of an upper-tailed one-sample t test in terms of F.b. Repeat part (a) for the two-tailed one sample t test.
An aspirin manufacturer fills bottles by weight rather than by count. Since each bottle should contain 100 tablets, the average weight per tablet should be 5 grains. Each of 100 tablets taken from a very large lot is weighed, resulting in a sample average weight per tablet of 4.87 grains and a
Let μ denote true average serum receptor concentration for all pregnant women. The average for all women is known to be 5.63. The article “Serum Transferrin Receptor for the Detection of Iron Deficiency in Pregnancy” (Amer. J. Clin. Nutrit. 1991: 1077– 1081) reports that P-value > .10 for
Scientists have recently become concerned about the safety of Teflon cookware and various food containers because perfluorooctanoic acid (PFOA) is used in the manufacturing process. An An article in the July 27, 2005, New York Times reported that of 600 children tested, 96% had PFOA in their blood.
The authors of the article “Luck of the Draw: Creating Chinese Brand Names” (J. of Advertising Res. 2008: 523–530) counted the number of “strokes” in the characters for the names of 1202 Chinese brand names. Certain totals for the number of strokes are considered lucky in Chinese culture,
A university library ordinarily has a complete shelf inventory done once every year. Because of new shelving rules instituted the previous year, the head librarian believes it may be possible to save money by postponing the inventory. The librarian decides to select at random 1000 books from the
Natural cork in wine bottles is subject to deterioration, and as a result wine in such bottles may experience contamination. The article “Effects of Bottle Closure Type on Consumer Perceptions of Wine Quality” (Amer. J. Enology Viticulture 2007: 182–191) reported that in a tasting of
State DMV records indicate that of all vehicles undergoing emissions testing during the previous year, 70% passed on the first try. A random sample of 200 cars tested in a particular county during the current year yields 124 that passed on the initial test. Does this suggest that the true
Show that when μ = μ' the one-sample t statistic (9.2) has a noncentral t distribution with n – 1 df and noncentrality parameter d given by (9.4).Equation 9.2 and 9.4 T= X - Ho S/√n (9.2)
Suppose that X, the fraction of a container a.b.c. If n = 50, what is the (approximate) value of c for which the test has significance level .05? that is filled, has pdf f(x;0) = 0x1 for 0 < x < 1 (where 0 > 0), and let X₁, ..., X₁ be a random sample from this distribution.
Suppose that each of n randomly selected individuals is classified according to his/her genotype with respect to a particular genetic characteristic and that the three possible genotypes are AA, Aa, and aa with long-run proportions (probabilities) θ2, 2θ(1 − θ), and (1 − θ)2, respectively
The error in a measurement is normally distributed with mean μ and standard deviation 1. Consider a random sample of n errors, and show that the likelihood ratio test for Ho: μ = 0 versus Ha: #0 rejects the null hypothesis when either x ≥c or x-c. What is c for a test with α = .05? How
Measurement error in a particular situation is normally distributed with mean value l and standard deviation 4. Consider testing H0: μ = 0 versus Ha: μ ≠ 0 based on a sample of n = 16 measurements.a.b.c. What is the power of the test proposed in (b) when μ = .1 and when μ = −.1?d. Calculate
This exercise establishes the “duality” between confidence intervals/bounds and hypothesis tests for the one-sample t procedures. a.b.c. Consider the lower-tailed t test of Ho: Mo versus Ha:
The test statistic in the Neyman–Pearson Lemma and the likelihood ratio test statistic K are intimately related. Consider testing H0: θ = θ0 versus Ha: θ = θa, and let Λ* denote the test statistic in (9.6). Show thatEquation (9.6) f(x1,..., Xn; Oa) * ƒ ( x ₁ , . . . , x n ; 00 ) ≥
A test of whether a coin is fair will be based on n = 50 tosses. Let X be the resulting number of heads. Consider two rejection regions: R1 = {x: either x ≤ 17 or x ≥ 33} and R2 = {x: either x ≤ 18 or x ≥ 37}.a. Determine the significance level (type I error probability) for each
Use the bootstrap hypothesis-testing method described in this section to test H0: μ = 1.5 versus Ha: μ ≠ 1.5 for the alcohol content data presented in Exercise 22.Data From Exercise 22 The industry standard for the amount of alcohol poured into many types of drinks (e.g., gin for a gin and
When a drug is recalled for safety concerns (e.g., too many people having serious adverse reactions), the pharmaceutical company making the drug can only re-issue it by convincing the FDA that the reformulated version of the drug is safer than the original version.a. In words, what are the null and
To test the ability of auto mechanics to identify simple engine problems, an automobile with a single such problem was taken in turn to 72 different car repair facilities. Only 42 of the 72 mechanics who worked on the car correctly identified the problem. Does this strongly indicate that the true
After a period of apprenticeship, an organization gives an exam that must be passed to be eligible for membership. Let p = P(randomly chosen apprentice passes). The organization wishes an exam that most but not all should be able to pass, so it decides that p = .90 is desirable. For a particular
A service station has six gas pumps. When no vehicles are at the station, let pi denote the probability that the next vehicle will select pump i (i = 1,2,…, 6). Based on a sample ofa. Show that the likelihood ratio test rejects H0 if either X ≥ c or X ≤ n − c.b. Let n = 10 and c = 9.
Consider testing a pair of simple hypotheses Ho: 0= 0o versus Ha: 0 = 0₁. Rather than prescribing the significance level and minimizing P(type II error), imagine trying minimize the linear combination a a+b ß for some specified constants a> 0 and b>0. Show that a a+b.ß is minimized by using the
Standard-size boxes for a particular brand of cereal indicate a net weight of 14 oz. A consumer group purchases a random sample of 50 such cereal boxes and weighs their contents. If the average of these 50 weights is 13.8 oz with a standard deviation of 1.1 oz, does the consumer group have
The error X in a measurement has a normal distribution with mean value 0 and variance σ2. Consider testing H0: σ2 = 2 versus Ha: σ2 = 3 based on a random sample X1, …, Xn of errors.a.b. For n = 10, find the value of c for the test in (a) that results in α = .05.c. Show that a
The article “Return Migration, Investment in Children, and Intergenerational Mobility: Comparing Sons of Foreign- and Native- Born Fathers” (J. Hum. Res. 2008: 299–324) presented the following summary data on years of education both for sample of sons of native-born fathers in Germany and
The accompanying time-to-repair (min) data for both high rail and low rail breaks on curved track appeared in the article “Uncertainty Estimation in Railway Track Life-Cycle Cost” (J. Rail Rapid Transit 2009: 285–293). (On a curved track, the high rail is the outer rail with the larger
Due to recent concerns about player concussions, football helmets have recently increased in both size and mass. Have these changes made a difference? The article “The Effects of Helmet Weight on Hybrid III Head and Neck Responses by Comparing Unhelmeted and Helmeted Impacts” (J. Biomech. Engr.
Much research has focused on comparing business environment cultures across several countries. The article “Perception of Internal Factors for Corporate Entrepreneurship: A Comparison of Canadian and U.S. Managers” (Entrep. Theory Pract. 1999: 9–24) presented the following summary data on
Returning to the previous exercise, the mean and standard deviation of the number of credit cards for the no-involvement group were 2.22 and 1.58, respectively, whereas the mean and standard deviation for the payment-help group were 2.09 and 1.65, respectively. Does it appear that the true average
Credit card spending and resulting debt pose very real threats to consumers in general, and the potential for abuse is especially serious among college students. It has been estimated that about two-thirds of all college students possess credit cards, and 80% of these students received cards during
Expert and amateur pianists were compared in a study “Maintaining Excellence: Deliberate Practice and Elite Performance in Young and Older Pianists” (J. Exp. Psychol. Gen. 1996: 331–340). The researchers used a keyboard that allowed measurement of the force applied by a pianist in striking a
Imaging of the colon with a contrast dye to evaluate for injury requires that the colon first be distended by pumping in carbon dioxide. The article “Determination of Normal Distribution of Distended Colon Volumes to Guide Performance of Colonic Imaging With Fluid Distention” (Curr. Probl.
A 2008 study in the J. Family Econ. Issues compared the work and home habits of female and male lawyers in Canada. All participants in the survey had at least one child; single parents and couples who are both lawyers were excluded. Two of the variables measured were the weekly number of hours
To decide whether chemistry or physics majors have higher starting salaries in industry, n B.S. graduates of each type are surveyed, yielding x̅ = $61;500 for chemistry and y̅ = $61;000 for physics. Assume σ = $2500 for both populations. Calculate the P-value for the appropriate two sample
Let μ1 and μ2 denote true average tread lives (miles) for two competing brands of size P205/65R15 tires.a.b. Test Ho: ₁-₂ = 0 versus Ha: M₁-M₂ 70 at level .05 using the following informa- tion: m = 45, x = 42,500, ₁ = 2200, n = 45, y = 40,400, and 2 = 1900.
What affects the time a consumer spends looking at a product on the shelf prior to selection? The following data summarized elapsed time (in seconds) for purchasers of fabric softener and washing-up liquid; the former is much more expensive than the latter. These products were chosen because
A study seeks to compare hospitals based on the performance of their intensive care units. The response variable variable is the mortality ratio, the ratio of the number of deaths over the predicted number of deaths based on the condition of the patients. The comparison will be between hospitals
According to a 2018 report by the CDC, the mean body mass index (BMI) for American adult men is 29.1 kg/m2, while the mean for women is 29.6 kg/m2. Suppose these are population averages.a. Let X̅ be the sample average BMI of 50 randomly selected American adult men Y̅ be the sample average BMI of
The article “Characterization of Bearing Strength Factors in Pegged Timber Connections” (J. Struct. Engr. 1997: 326–332) gave the following summary data on proportional stress limits for specimens constructed using two different types of wood:Assuming that both samples were selected from
Exercise 22 from Chapter 9 gave the following data on amount (oz) of alcohol poured into a short, wide tumbler glass by a sample of experienced bartenders 2.00, 1.78, 2.16, 1.91, 1.70, 1.67, 1.83, 1.48. The cited article also gave summary data on the amount poured by a different sample of
Which factors are relevant to the time a consumer spends looking at a product on the shelf prior to selection? The article “Effects of Base Price upon Search Behavior of Consumers in a Supermarket” (J. Econ. Psychol. 2003: 637–652) reported the following data on elapsed time (sec) for fabric
The article “Gender Differences in Individuals with Comorbid Alcohol Dependence and Post-Traumatic Stress Disorder (Am. J. Addict. 2003: 412–423) reported the accompanying data on total score on the Obsessive-Compulsive Drinking Scale (OCSD).Formulate hypotheses and carry out an appropriate
Is the incidence of head or neck pain among video display terminal users related to the monitor angle (degrees from horizontal)? The paper, “An Analysis of VDT Monitor Placement and Daily Hours of Use for Female Bifocal Users” (Work 2003: 77–80), reported the accompanying data. Carry out an
For the data of the previous two exercises, we want a 95% confidence interval for the ratio of population standard deviations. Previous Exercise a. Recall that this method requires the data to be normal, and the method is sensitive to departures from normality. Check the data for normality to
For the data of the previous exercise, now consider testing the hypothesis of equal population variances.a. Carry out a two-tailed test using the method of Section 10.5. Recall that this method requires the data to be normal, and the method is sensitive to departures from normality. Check the data

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