All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Hire a Tutor
AI Study Help New

Search
Sign In
Register

study help
business
fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

Consider thefamilyofgammadistributionswithidenticalparameters for shapeandscale,i.e.withdensitieswith respecttostandardLebesguemeasureon R+, andlet X1, ...,Xn be asample from thisdistribution.a)
Consider thefamilyofdistributionswithdensitieswith respecttostandardLebesguemeasureon R and considerasample X1, ...,Xn from thisdistribution.a) Determineamomentestimator ˜θn for θ based
Consider thefamilyofParetodistributionswithdensitieswith respecttostandardLebesguemeasureon R and assume α > 2 butunknown.Consider asample X1, ...,Xn from thisdistribution.a)
Consider asample Z1, ...,Zn of independentandidenticallydistrib-uted randomvariables,where Zi = Xi − Yi with Xi and Yi independent andexpo-nentially distributedwithmean θ.a) Showthat Eθ(Z4 i )
Consider thesimpleBernoullimodelwhereX1, ...,Xn are independ-ent andidenticallydistributedwithwith μ ∈ (0, 1) being unknown.a) ShowthattheMLEof μ is ˆμn = ¯Xn and
Consider theestimatorof thevariance σ2 in thesimplestandardnormalmodel,sothat S2n is distributedas S2n ∼ σ2χ2(n − 1)/(n − 1).a) Showthat S2n is asymptoticallynormallydistributedwithb)
Consider Xn = (Y1+· ··+Yn), where Y1, ...,Yn are independent and identicallyPoissondistributedwithparameter μ ∈ R+ so thatUse thedeltamethodtoshowthatand contrastthiswiththefactthat X−1 n
Consider thefamilyofgammadistributionswithidenticalparameters for shapeandscale,i.e.withdensitieswith respecttostandardLebesguemeasureon R+ as inExercise3.7.Showthatthe MLE of β is
Consider asample Z1, ...,Zn of independentandidenticallydistrib-uted randomvariables,where Zi = Xi − Yi with Xi and Yi independent andexpo-nentially distributedwithmean θ.a)
Let X = (X1, ...,Xn) be independentandPoissondistributedwith E(Xj) = λNj where λ > 0 is unknownand Nj are knownconstants.Modelsofthistypearise,for example,inriskstudieswhere Nj is
Let X = (X1, ...,Xn) be asampleofsize n from theuniformdistri-butionontheinterval (μ − δ,μ + δ) with densitywith respecttostandardLebesguemeasureon R, where θ = (δ,μ) ∈ Θ = R+ × R with
Let X1, ...,Xn be independentwithmeans E(Xi) = μ + βi and variances V(Xi) = σ2 i . Suchasituationcould,forexampleoccurwhen Xi are estimators of μ obtained fromindependentsourcesand βi is the
The standardestimatorin thenormaldistributionisdistributedas S2n ∼ σ2χ2(n − 1)/(n − 1) and thus unbiased forthevariance σ2, butnotfortheprecision ρ2 = 1/σ2, norforthestandard deviation σ,
Let X and Y be independentandexponentiallydistributedwith E(X) = λ og E(Y ) =3λ. Considerthefollowingtwoestimatorsof λ: is thegammafunction.a) Whichoftheseestimatorsareunbiasedestimatorsof λ?b)
Consider thefamilyofgammadistributionswithidenticalparameters for shapeandscale,i.e.withdensitieswith respecttostandardLebesguemeasureon R+.a)
Let (X,Y ) be randomvariablestakingvaluesin R+ × N0 with a distributiondeterminedasfollows: X is drawnfromanexponentialdistributionwith mean λ yielding thevalue x, andsubsequently Y is
Let (X,Y ) be randomvariablestakingvaluesin N0 × R+ with a distributiondeterminedasfollows:X is drawnfromaPoissondistributionwithmeanλ yielding thevalue x and subsequently Y is
The inversenormaldistribution has densitywith respecttostandardLebesguemeasureon R+. Youmaywithoutproofassume that R∞0 fμ,λ(x) dx = 1 for all (μ, λ) ∈ R2 +. Letnowwhere Pμ,λ has
Consider thefamilyofParetodistributionswithdensitieswith respecttostandardLebesguemeasureon R, where α > 0 is unknown.Rep-resent thisfamilyasaregularexponentialfamilyofdimension1andidentifybase
Consider thefamilyofnegativebinomialdistributions,i.e.distribu-tions ofarandomvariable X with densitieswith respecttocountingmeasureon N0 = 0, 1, .... Here r ∈ N is consideredfixed and
Let X ∼ N3(0,Σρ) where −1 a) Showthatthespecificationabovedefinesaregularnormaldistributionon R3.b) Showthattheconcentrationmatrix Kρ is givenasc) Letnow L be
Let X ∼ N3(ξ,σ2I3) whereFurther,let L be thelinearsubspaceof R3 determined asa) Determine ΠLX and finditsdistribution.b) Findthedistributionof ∥X − ΠLX∥2, where ∥·∥ denotes
Let X = (X1,X2,X3)⊤ followanormaldistributionon R3 with expectation 0 and covariancematrixwhere a ∈ R.a) Forwhichvaluesof a is Σ(a) a validcovariancematrix?b) Whatisthedistributionof Y = 2X1 −
Let X ∼ N2(0, Σ) wherea) Showthatthedistributionof X is singular.b) Identifythesupportofthedistribution.c) Findallvalidconcentrationoperators K for X. = 1 2 2 4
Let X ∼ N3(0, I3) and define Y = a + BX, wherea) Whatisthedistributionof Y ?b) Whichofthepairs (Y1, Y2), (Y1, Y3), and (Y2, Y3) are independent?c) Showthatthedistributionof Y is
Let X = (X1,X2)⊤ followanormaldistributionon R2 with expect-ation 0 and covariancematrixwhere a ∈ R.a) Forwhichvaluesof a is Σ(a) a validcovariancematrix?b) Forwhichvaluesof a is
Let X ∼ N2(ξ, Σ) whereand define Y ∈ R2 by Y1 = X2 − X1 and Y2 = X1 − 1.a) Arguethat X has adensitywithrespecttoLebesguemeasureon R2.b) Findtheconcentrationmatrix K of X.c)
Let X ∼ N3(ξ, Σ) wherea) Arguethat X has adensitywith respect to Lebesguemeasureon R3.b) Find the distribution ofc) Findtheconcentrationmatrixforthedistributionof Y . => 43 1 38 1 2 1 1 2
Let X ∼ N3(ξ, Σ) wherea) Findthemarginaldistributionsof (X1,X2)⊤ and (X1,X3)⊤.b) Findthedistributionof (X2,X3,X1)⊤.c) Findthedistributionof Y = X1 − X2 + X3. 6 3 3 = 3 80 4 00 1
Consider theCauchymodelinExample1.9forthecasewhenthe scale parameter β = 1 is known.a) Determinethescoreandinformationfunction;b) InvestigatebysimulationwhetherBartlett’sidentitiesholdinthiscase.
Consider thefamilyofdistributionswithdensitieswith respecttostandardLebesguemeasureon R, where a(θ) is anormalizingcon-stant.a) Showthat a(θ) = θ;b) Showthat Y = −logX, where X has
Consider thefamilyofnegativebinomialdistributionsasinExer-cise 1.2anddeterminethescore,informationfunction,Fisherinformation,andquad-ratic scoreinasuitableparametrization.
Consider thefamilyoflog-normaldistributionsasinExercise1.3and determine thescore,informationfunction,Fisherinformation,andquadraticscore when parametrizedwiththemeanandcoefficientofvariation.
Consider thesimplenormalmodelasinExercise1.1anddetermine the score,informationfunction,Fisherinformation,andquadraticscorewhenpara-metrized withmeanandcoefficientofvariation.
Consider thesimplePoissonmodel,parametrizedwiththenullfraction as inExample1.10anddeterminethescore,informationfunction,Fisherinforma-tion, andquadraticscoreinthisparametrization.
Consider thesimplenormalmodelinExample1.5anddeterminethe score, informationfunction,Fisherinformation,andquadraticscoreintheparamet-rization usingthemean ξ and standarddeviation σ.
If Y = logX and Y ∼ N(ξ,σ2), X is saidtohavea log-normal distribution.Identifythemeanandcoefficientofvariationinthisdistributionand parametrize thefamilywiththesequantities.
A drawing pin is throwns everaltimesatrandomuntilithaslanded fivetimesflatonitshead,andthetotalnumberofthrowsneededtoachievethisis recorded.
Consider thesimplenormalmodelinExample1.5withthemodifica-tion thatthemean ξ is restrictedto ξ ∈ R+ and reparametrizethemodelintermsof the meanandcoefficientofvariation C(X) V(X)/E(X).
+ C. Post-Data Analysis 1. Determine and interpret the estimated effect size using Cramer’s V.2. Determine and interpret the power of the study from a post hoc perspective.3. Present at least two
+ B. Data Analysis 1. Conduct a hypothesis test using the chi-square test for independence by applying all four steps of hypothesis testing as presented in Section 12.5. The data file “Ch_12
+ A. Pre-Data Analysis 1. Specify the research questions and corresponding operational definitions.2. Specify the research hypotheses.3. Determine the appropriate research methodology/design and
C. Post-Data Analysis 1. Determine and interpret the estimated effect size using Cohen’s w.2. Determine and interpret the power of the study from a post hoc perspective.3. Present at least two
B. Data Analysis 1. Conduct a hypothesis test using the chi-square test for goodness of fit by applying all four steps of hypothesis testing as presented in Section 12.3.This research study is an
A. Pre-Data Analysis 1. Specify the research questions and corresponding operational definitions.2. Specify the research hypotheses.3. Determine the appropriate research methodology/design and
10. Three major airports, as listed by the U.S. Bureau of Transportation Statistics (BTS, 2022), were randomly selected and the number of flight delays was recorded with respect to BTS’ categories
9. Let’s assume that an aviation researcher hypothesized that the proportion of runway incursions would be uniform across four different runway incursion categories: (a)those attributed to air
8. Referencing Item 6 above, suppose the researcher organized and analyzed the data from the perspective shown below. Would the analysis yield the same chi-square value as reported in Item 6?a. Yes,
7. Referencing Item 6 above, are the observed results inconsistent with the expected ratio at the 1% level of significance?a. Yes, because χ2* > χ2 critical.b. Yes, because χ2* < χ2 critical.c.
6. An aviation researcher examined whether airport executives (AEs) and aviation maintenance technicians (AMTs) also had a PPL. A random sample yielded the following data:Data analysis resulted in
5. A group of 100 flight students and 100 nonflight students was asked to reply to the question, "In general do you enjoy reading a college textbook?" The results are given below. What would be the
4. If the observed and expected frequencies are equal, then the x test statistic will bea. positiveb. zeroc. negatived. infinitely large
3. Which of the following situations is true for the chi-square test for goodness of fit?a. A small number of categories most likely will lead to a large x.b. A large number of categories most likely
2. If a chi-square test for goodness of fit results in a large chi-square value that is statis- tically significant, then this means that thea. observed frequencies are consistent with the expected
1. One of the differences between one-way chi-square and two-way chi-square is:a. One-way chi-square involves scores on one variable whereas two-way chi-square involves scores on two variables.b.
Distinguish between a parametric vs. a nonparametric test.
1. When a repeated-measures t test is used to compare pre- and post-assessment scores, the following relationship with respect to sample size (n) is expected: a. npre> npost b. npre=npost C. npre
DeterminetheMLEof λ and identifywhenitiswell-defined.
Let X and Y be independentrandomvariableswith X Poisson dis-tributedwithmean λ and Y exponentiallydistributedwithrate λ, where λ > 0 as in
Showthattheestimator ˆθ under b)inExercise4.4isaMLE.
125 Testing a new insecticide. Traditionally, people protect themselves from mosquito bites by applying insect repellent to their skin and clothing. Recent research suggests that peremethrin, an
123 Short-day traits of lemmings. Many temperate-zone animal species exhibit physiological and morphological changes when the hours of daylight begin to decrease during the autumn months. A study was
107 Accounting and Machiavellianism. A study of Machiavellian traits in accountants was published in Behavioral Research in Accounting (Jan. 2008).Machiavellian describes negative character traits
103 Why does the experimentwise error rate of a multiplecomparison procedure differ from the significance level for each comparison (assuming that the experiment has more than two treatments)?
102 What are the treatments in a two-factor experiment with factor A at three levels and factor B at two levels?
101 Explain the difference between an experiment that utilizes a completely randomized design and one that utilizes a randomized block design.
100 What is the difference between a one-way ANOVA and a two-way ANOVA?
98 Testing a new pain-relief tablet. Refer to the Tropical Journal of Pharmaceutical Research (June 2003) study of the impact of binding agent, binding concentration, and relative density on the mean
97 Eyewitnesses and mug shots. When an eyewitness to a crime examines a set of mug shots at a police station, the photos are usually presented in groups (e.g., 6 mug shots at a time). Criminologists
92 Virtual-reality–based rehabilitation systems. In Robotica(Vol. 22, 2004), researchers described a study of the effectiveness of display devices for three virtual-reality(VR)-based hand
87 Egg shell quality in laying hens. Introducing calcium into a hen’s diet can improve the shell quality of the eggs laid.One way to do this is with a limestone diet. In Animal Feed Science and
85 Suppose a 3 * 3 factorial experiment is conducted with three replications. Assume that SS(Total) = 1,000.For each of the following scenarios, form an ANOVA table, conduct the appropriate tests,
81 Suppose you conduct a 3 * 5 factorial experiment.a. How many factors are used in this experiment?b. Can you determine the type(s) of factors—qualitative or quantitative—from the information
80 Describe what is meant by factor interaction.
79 What conditions are required for valid inferences from a factorial ANOVA?
78 What is a balanced factorial design?
77 Describe how the treatments are formed in a complete factorial experiment.
Refer to Example 10 . Suppose the same factorial experiment is performed on four other brands (E, F, G, and H), and the results are as shown in Table 16 . Repeat the factorial analysis and interpret
74 Absentee rates at a jeans plant. A plant that manufactures denim jeans in the United Kingdom recently introduced a computerized automated handling system.The new system delivers garments to the
73 Plants and stress reduction. Plant therapists believe that plants can reduce the stress levels of humans. A Kansas State University study was conducted to investigate this phenomenon. Two weeks
66 Making high-stakes insurance decisions. The Journal of Economic Psychology (Sept. 2008) published a study on high-stakes insurance decisions. In part A of the experiment, 84 subjects were informed
64 Suppose an experiment utilizing a randomized block design has four treatments and nine blocks, for a total of 4 * 9 = 36 observations. Assume that the total sum of squares for the response is
61 What conditions are required for valid inferences from a randomized block ANOVA design?
60 When is it advantageous to use a randomized block design over a completely randomized design?
59 Explain the difference between a randomized block design and a paired difference experiment.
Refer to Examples 4–6. Suppose the USGA wants to compare the mean distances associated with the four brands of golf balls struck by a driver, but wishes to employ human golfers rather than the
57 Restoring self-control while intoxicated. Refer to the Experimental and Clinical Psychopharmacology (Feb.2005) study of restoring self-control while intoxicated, presented in Exercise 34 . The
55 Estimating the age of glacial drifts. Refer to the American Journal of Science (Jan. 2005) study of the chemical makeup of buried tills (glacial drifts) in Wisconsin, presented in Exercise 37 .
54 Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of treatments for children’s cough symptoms, Exercise 35 .The data are saved in the
53 Dental fear study. Does recalling a traumatic dental experience increase your level of anxiety at the dentist’s office? In a study published in Psychological Reports (Aug.1997), researchers at
50 A new dental bonding agent. Refer to the Trends in Biomaterials & Artificial Organs (Jan. 2003) study of a new bonding adhesive for teeth, presented in Exercise 30.A completely randomized design
45 A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown here. Rank the means from smallest to largest. Which means are significantly
44 Consider a completely randomized design with five treatments:A, B, C, D, and E. The ANOVA F -test revealed significant differences among the means. A multiple-comparison procedure was used to
43 Consider a completely randomized design with k treatments. Assume that all pairwise comparisons of treatment means are to be made with the use of a multiplecomparison procedure. Determine the
42 Give a situation when it is most appropriate to apply Tukey’s multiple-comparison-of-means method.
41 For each of the following confidence intervals for the difference between two means, (m1 - m2), which mean is significantly larger?a. (-10, 5)b. (-10, -5)c. (5, 10)
40 Define a comparison wise error rate.
39 Define an experiment wise error rate.
Refer to the completely randomized design of Example 4 , in which we concluded that at least two of the four brands of golf balls are associated with different mean distances traveled when struck
31 Robots trained to behave like ants. Robotics researchers investigated whether robots could be trained to behave like ants in an ant colony ( Nature , Aug. 2000). Robots were trained and randomly

Showing 200 - 300 of 3444

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved