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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

30 A new dental bonding agent. Trends in Biomaterials &Artificial Organs (Jan. 2003) Conducted a study of a new bonding adhesive for teeth. The new adhesive (called“Smartbond”) has been developed
29 College tennis recruiting with a team Web site. Most university athletic programs have a Web site with information on individual sports and a Prospective Student Athlete Form that allows high
28 Whales entangled in fishing gear. Entanglement of marine mammals (e.g., whales) in fishing gear is considered a significant threat to the species. A study published in Marine Mammal Science (April
27 Treating cancer with yoga. According to a study funded by the National Institutes of Health, yoga classes can help cancer survivors sleep better. The study results were presented at the June 2010
25 Suppose the total sum of squares for a completely randomized design with p = 5 treatments and n = 30 total measurements(6 per treatment) is equal to 500. In each of the following cases, conduct an
22 Refer to Exercise 21. Conduct a two-sample t -test of the null hypothesis that the two treatment means are equal for each dot plot. Use a = .05 and two-tailed tests. In the course of the test,
20 Find the following probabilities:a. P(F … 3.48) for v1 = 5, v2 = 9b. P(F 7 3.09) for v1 = 15, v2 = 20c. P(F 7 2.40) for v1 = 15, v2 = 15d. P(F … 1.83) for v1 = 8, v2 = 40
19 Use Tables VIII , IX , X , and XI of Appendix: Tables to find each of the following F values:a. F.05, v1 = 3, v2 = 4b. F.01, v1 = 3, v2 = 4c. F.10, v1 = 20, v2 = 40d. F.025, v1 = 12, v2 = 9
17 What conditions are required for a valid ANOVA F -test in a completely randomized design?18 True or False . The ANOVA method is robust when the assumption of normality is not exactly satisfied in
16 Explain the concept of a balanced design.
15 Explain how to collect the data for a completely randomized design.
Refer to the completely randomized ANOVA design conducted in Example 4 .Are the assumptions required for the test approximately satisfied?
Suppose we want to compare the taste preferences of consumers for three different brands of bottled water (say, Brands A, B, and C), using a random sample of 15 consumers of bottled water. Set up a
14 Testing a new pain-relief tablet. Paracetamol is the active ingredient in drugs designed to relieve mild to moderate pain and fever. The properties of paracetamol tablets derived from khaya gum
13 Baker’s versus brewer’s yeast. The Electronic Journal of Biotechnology (Dec. 15, 2003) published an article comparing two yeast extracts: baker’s yeast and brewer’s yeast. Brewer’s yeast
12 Exam performance study. In Teaching of Psychology(Aug. 1998), a study investigated whether final exam performance is affected by whether or not students take a practice test. Students in an
11 Taste preferences of cockatiels. Applied Animal Behaviour Science (Oct. 2000) published a study of the taste preferences of caged cockatiels. A sample of birds bred at the University of California
10 Treatment for tendon pain. Chronic Achilles tendon pain(i.e., tendinosis) is common among middle-aged recreational athletes. A group of Swedish physicians investigated the use of heavy-load
9 Back/knee strength, gender, and lifting strategy. Human Factors (December 2009) investigated whether back and knee strength dictates the load-lifting strategies of males and females. A sample of 32
8 Extinct New Zealand birds. Refer to the Evolutionary Ecology Research (July 2003) study of extinction in the New Zealand bird population, presented in Exercise 18.Recall that biologists measured
7 Treating depression with a combination of drugs. Physicians are now experimenting with using a combination of drugs, rather than a single drug, to treat major depression. In a study published in
6 Health risks to beachgoers. According to a University of Florida veterinary researcher, the longer a beachgoer sits in wet sand or stays in the water, the higher the risk of gastroenteritis (
5 Identifying the type of study. Determine whether each of the following studies is observational or designed, and explain your reasoning:a. An economist obtains the unemployment rate and gross state
4 What are the experimental units on which each of the following responses are observed?a. GPA of a college studentb. Household incomec. Your time in running the 100-yard dashd. A patient’s
3 What is the difference between an observational and a designed study?
2 What are the treatments for a designed study with two factors, one qualitative with two levels (A and B) and one quantitative with five levels (50, 60, 70, 80, and 90)?
1 What are the treatments for a designed study that utilizes one qualitative factor with four levels: A, B, C, and D?
Suppose the USGA is also interested in comparing the mean distances the four brands of golf balls travel when struck by a five-iron and by a driver. Ten balls of each brand are randomly selected,
The United States Golf Association (USGA) regularly tests golf equipment to ensure that it conforms to the association’s standards. Suppose the USGA wishes to compare the mean distances traveled by
Discuss the critical elements in the design of a sampling experiment
Let (X1, Y1, ...,Yn,Xn) be independentandexponentiallydistrib-uted randomvariableswhere Xj and Yj havedensitieswithrespecttostandard Lebesque measure:fj(x; θ) = jθe−jθx, x> 0, gj(y; λ) =
Let X and Y be independentandexponentiallydistributedrandom variableswith E(X) = β and E(Y ) =1/β where β > 0.a) Representthefamilyofjointdistributionsof (X,Y ) as acurvedexponentialfam-ily
Let X and Y be independentrandomvariableswith X Poisson’sdis-tributedwithmean λ and Y exponentiallydistributedwithrate λ, where λ > 0.a) Representthefamilyofjointdistributionsof (X,Y ) as
Let X and Y be independentandexponentiallydistributedrandom variableswith E(X) = μ and E(Y ) =2μ, where μ > 0. Representthefam-ily ofjointdistributionsof (X,Y ) as
Let X and Y be independentandexponentiallydistributedrandom variableswith E(X) = β and E(Y ) =1/β where β > 0 as inExercise5.10andlet(X1, Y1), ..., (Xn, Yn) be asamplefromthisdistribution.a)
The von Misesdistribution is adistributionontheunitcircleor,equi-valently,theinterval (−π,π] with density fκ,θ(x) = eκ cos(x−θ)2πIo(κ)with
The Weibulldistribution with shapeparameter α > 0 has density function fα(x) = αxα−1e−xαwith respecttostandardLebesguemeasureon R+. TheWeibulldistributionis,for
A clinicaltrialistobeconductedwithanewmedicineforcontrolling hypertension.Atotalof 2n patients whosufferfromhighbloodpressurewillberan-domized
Suppose amultiplechoiceexamistobeconstructed,withfourpos-sible answersineachcategory.Ifwemakeitapasscriterionthat62.5%oftheques-tions mustbecorrectlyanswered,howmanyquestionsdoweneedtoensurethata
Consider thesituationwithpairedcomparisonsasin Section 7.6.2.4.Showthatthesuggestedtestbasedondifferencesisequivalenttothelikelihoodratio test
Consider comparingmeansasin Section 7.6.2.3 and showthatthetest described isequivalenttothelikelihoodratiotestwhenvariancesinthegroupsare assumed
Showthatthesimple T-test in Section 7.6.2.2 is equivalenttothe likelihoodratiotestinasuitablelinearnormalmodel.
Let’s assume a commercial airline recorded the fuel burn from takeoff to landing for all the routes it flew over the past 2 years and the fuel usage was normally distributed. Let’s further assume
Let’s assume that a private jet manufacturer in North America wants to design seats in its aircraft so they are wide enough to fit most men. Let’s further assume that the design engineers use
1. If the scores on an exam were approximately normally distributed and your score was one standard deviation above the mean, then you probably scored better than of those taking the exam.a. 50%b.
2. Which of the following is true for a normal distribution?a. Around 30% of the scores will be located within one standard deviation of the mean.b. Around 50% of the scores will be located within
3. Which of the following is NOT true of the normal curve?a. It is useful for estimating what percent of scores will fall above and below certain points.b. The mode is equal to the median.c. The
4. Lauren is enrolled in a very large Aviation Psychology class. On the first exam, the class mean was M = 75 (SD = 10), and on the second exam, the class mean was M2 = 70 (SD = 15). Lauren scored 85
5. Consider the table below, which reports the number of U.S. airports and the number of meters of runways that are either paved (The World Factbook, 2021a) or unpaved (The World Factbook, 2021b). If
6. The population (2, 3, 5, 7} has mean = 4.25 and standard deviation = 1.92. When sampling with replacement, there are 16 different possible ordered samples of size n = 2 that can be selected from
7. The researcher of a human aviation factors study involving "round dial" equipped aircraft reported that the distribution of the diameters of the round dials was approx- imately normal with a
8. The standard error of the mean serves as a rough indicator of the average amount by which sample means deviate froma. the population mean.b. the one observed sample mean.c. some population
9. In a hypothetical study, let's assume that an aviation safety officer conducted a na- tionwide survey of flight schools and reported that approximately 4% of the flight schools' training fleet had
10. A negative z score signifies that the original score isa. less than the meanb. negativec. the opposite of the meand. a small number
1. Let's assume the manager of a fixed-base operator (FBO) asked the pilots who used the FBO's services to specify their age. After collecting data for 6 months, the results approximated a normal
2. Let's assume that the College of Aeronautics at a local university administers a col- lege placement test of mathematical ability (CPT-MA) at the beginning of each fall se- mester to incoming
3. According to the U.S. Department of Health and Human Services (2021), the poverty rate for a four-person household in 2021 was $26,500. To bring attention to how low salaries are for first
4. An aircraft maintenance aptitude test has mean = 300 and standard deviation = 25. If the scores approximate a normal distribution, what score would be at the upper quartile?
5. A common design requirement for aircraft seats is they must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. If this requirement is adopted,
6. What is the research question for this study?In response to an increase in the number of pilot deviation (PD) runway incursions (RIs) among general aviation (GA) pilots 65 years or older, an
7. What are the independent and dependent variables? In response to an increase in the number of pilot deviation (PD) runway incursions (RIs) among general aviation (GA) pilots 65 years or older, an
8. Let's assume the researcher randomly selects a 73-year-old GA pilot, has him take the supplement daily for 6 months, and then administers the memory test. If the pilot memorizes all 12 digits in
9. Does it appear that the supplement influences memory capacity? Explain. In response to an increase in the number of pilot deviation (PD) runway incursions (RIs) among general aviation (GA) pilots
10. If the researcher wants to identify the 10% of the 65-year-old or older population that takes the longest time to complete the memory test, what minimum time defines this group? In response to an
11. As part of a study involving the international travel and tourism industry, Abdullah (2019) examined the relationship between the 14 factors of the travel and tourism competitiveness index (TTCI)
Write research, null, and alternative hypotheses for a research study.
Open the data file Ch_4 CFI Complacency Scores, which contains the complacency scores from the file Ch_3 Standard Normal Distribution from Chapter 3. Use your statistics program to produce a set of
Use the CFI complacency scores from Example 4.1 to determine the sample size needed to estimate the mean complacency score of the population of CFIs in the United States if we want to be accurate
Given the descriptions in a–c, write the research, null, and alternative hypotheses.a. Refer to Example 4.1. Let’s assume that the mean complacency score in the popu-lation of CFIs is μ = 20,
What Is Statistical Significance?
Continuing with the BIM example, let’s assume that 100 flight students prepared for the IRA exam using BIM’s software. The data file Ch_4 Example 4.4 contains the corresponding hypothetical exam
1. Which of the following statements describes the role of the null hypothesis in research?a. It enables researchers to determine if there is a real relationship between variables.b. It enables
2. If the results of a research study are statistically significant, then this means that the resultsa. are extremely important relative to the context of the research setting.b. most likely also
3. Any shift to a Cl with a higher degree of confidence produces aa. wider, less precise Cl.b. wider, more precise Cl.c. narrower, less precise Cl.d. narrower, more precise Cl.
4. As sample size increases, a Cl approachesa. standard errorb. population rangec. point estimated. infinity
5. If Ho is true, then the hypothesized and true sampling distributions willa. differb. have a mean of zeroc. overlapd. be the same
6. Let's assume we conduct a hypothesis test where we eliminate the rejection region that is, instead of a = .05 or a = .01, we set a = 0 or let a approximately equal 0. What do you think will
7. The analysis of a random sample of 500 pilots who fly into and out of JFK indicates that a 98% CI for their mean annual income is [$41,300, $58,630]. Could this informa- tion be used to conduct a
8. A researcher collected data from a random sample of 50 flight students to create a Cl to estimate the mean time to PPL. Let's assume that the sample mean time to PPL does not change. Which of the
9. Let's assume Gleim claims that students who use its software to prepare for the FAA IRA exam will score above the national average. To test this claim, a researcher ran- domly selects 100 flight
10. Goldberg and Williams' (1988) General Health Questionnaire (GHQ) is a 12-item in- strument that measures psychological distress such as depression and anxiety. Scores could range from 0 to 36,
1. Write the corresponding RQ and research hypothesis and include any needed opera- tional definitions.Let's assume a published op-ed article by a critic of low-cost carriers (LCCs) claims that the
2. Formulate Ho and H, in words and symbols relative to the researcher's belief. Let's assume a published op-ed article by a critic of low-cost carriers (LCCs) claims that the aircraft LCCs fly are
3. Identify the test criteria that correspond to the hypothesis test. Let's assume a published op-ed article by a critic of low-cost carriers (LCCs) claims that the aircraft LCCs fly are at least 12
4. Compute the test statistic. Let's assume a published op-ed article by a critic of low-cost carriers (LCCs) claims that the aircraft LCCs fly are at least 12 years old and therefore are too old and
5. Determine if you will reject or fail to reject Ho and explain why. As part of your re- sponse, determine and interpret the p value.
6. Report and interpret the ES. Let's assume a published op-ed article by a critic of low-cost carriers (LCCs) claims that the aircraft LCCs fly are at least 12 years old and therefore are too old
7. Report and interpret the 95% CI. Let's assume a published op-ed article by a critic of low-cost carriers (LCCs) claims that the aircraft LCCs fly are at least 12 years old and therefore are too
8. Explain what it would mean if the researcher committed a Type I or Type II error. Let's assume a published op-ed article by a critic of low-cost carriers (LCCs) claims that the aircraft LCCs fly
9. Write a concluding comment about the findings relative to the critic's claim as well as with respect to what you hypothesized. Let's assume a published op-ed article by a critic of low-cost
10. What is one plausible explanation for the results?Let's assume a published op-ed article by a critic of low-cost carriers (LCCs) claims that the aircraft LCCs fly are at least 12 years old and
Let’s revisit Example 4.1 from Chapter 4, which involved constructing the 95% CI for the mean CFI complacency score based on the data given in the file Ch_4 CFI ComplacencyScores. Recall from
9. A flight test engineer endeavors to estimate the mean Mach Number of a par- ticular model aircraft. (Note: Mach Number = Aircraft Speed divided by the speed of sound, where the speed of sound is a
10. Research studies of melatonin, an over-the-counter sleep aid supplement, have shown that it can reduce the amount of time it takes to fall asleep. Let's assume that a causal-comparative study
Compare the p-valuefortheexactconditionaltestinthescreenglare examplein Section 8.3.4.3 with asymptotic p-valuesusingthe G2 and X2 statistics.
Calculate a95%confidenceintervalfortherelativeriskofgetting myocardial infarctionwhenusingaspirinascomparedtoplaceboinExample8.6.
Let X and Y be independentandexponentiallydistributedrandom variableswith E(X) = β and E(Y ) =1/β where β > 0 as inExercise3.9and Exercise4.10,andlet (X1, Y1), ..., (Xn, Yn) be
Let X and Y be independentrandomvariableswith X Poissons dis-tributedwithmean λ and Y exponentiallydistributedwithrate λ, where λ > 0, and let (X1, Y1), ..., (Xn, Yn) be
Let X1, ...,Xn, ... and Y1, ...,Yn, ... be asequenceofreal-valued random variablessothat plimn→∞ Xn = 0 and |Yn| ≤ C, where C is apositive constant. Showthat plimn→∞ XnYn = 0.
C. Post-Data Analysis 1. Determine and interpret the estimated effect size using Cohen'sd. 2. Determine and interpret the effect size relative to explained variance (r). 3. Determine and interpret

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