Search

17 Jun 2019: Derive carefully the test of homogeneity and test the hypothesis that the distributions ofscores among students in the two cities are the same.

30 Aug 2019: yes. >> chisq.test(rbind(c(341,1775),c(82,238))). Pearson’s Chi-squared test. data: rbind(c(341, 1775), c(82, 238))X-squared = 16.8618, df = 1, p-value =

17 Jun 2019: 8]. 10E State the comparison and ratio tests for the convergence of a series.

30 Aug 2019: Part III, Paper 54. 5. 3 Satellite migrationConsider the dynamics of test particles around a satellite in the xy plane in the infiniteshearing sheet. ... 1 s2)3/2ds = 1.]. (b) If a disc of test particles has surface density Σ(x), show that, assuming a

17 Jun 2019: Explain carefully how the test should be implemented. 1/II/18C Statistics. Let X1,. ... yθ1eydy and θ > 1 is unknown. Find the most powerful test of size α,.

17 Jun 2019: It is desired to test the hypothesis H0 : λ = µ against H1 : λ 6= µ. ... Let w(θ) denote the power function of this test at θ (> 1).

17 Jun 2019: 8H StatisticsDefine a simple hypothesis. Define the terms size and power for a test of one simple. ... Calculate the power of your test. 9H OptimisationWhat does it mean to state that f : Rn R is a convex function?

30 Aug 2019: anova(eggs.glm1, test="Chisq"). Analysis of Deviance Table. Model: binomial, link: logit. ... Does itmake sense to test for the goodness of fit of model aom.glm2?

30 Aug 2019: H(2)0 : δ2 = µ2 µ0 6 0. (a) Write down the Wald test statistics W1 and W2 for testing H(1)0 and H. ... screening test every t years. The test may reveal that they have pre-clinical cancer, whichcan be treated before it progresses to clinical cancer.

30 Aug 2019: The courses arranged by the Statistical Laboratory are perhaps the most immediately transferable, but mathematics underpins all the Natural Sciences, Computer Science, Engineering, Economics, Business and Management Studies and a whole

17 Jun 2019: What is the result of applying this test at the 0.01 level? [ ... tostrength tests, the number out of the six blocks failing the test being recorded in thefollowing table:.

30 Aug 2019: Let W1 label the Wald test statistic of H0 for the first stage patients (i = 1,. , ... n),and W2 the Wald test statistic of H0 for the combined set of first and second stagepatients (i = 1,. ,

19 Jun 2019: c) Show how to calculate the sample size of persistent young offenders to be ran-domised between P30 and CSO180 if the Sentencing Commission wants to have80% power for a test

30 Aug 2019: 8. > anova(mod1,dispersion=1,test="Chisq"). Analysis of Deviance Table. Model: Gamma, link: inverse. ... pos 1 0.27603 57 18.185 0.5993. > anova(mod2,test="F"). Analysis of Deviance Table.

30 Aug 2019: Part III, Paper 23. 3. 2. (a) State precisely the first quantifier elimination test QET1 from the lecture (in words:“Suppose that if two models of T have a common substructure, ... Then T has quantifier elimination”). (b) Derive the following

19 Jun 2019: We wish to construct significance tests of size α, and sample sizes to achieve theright power, in helping Professor UK and others to design appropriate studies.

17 Jun 2019: test to test the hypothesis H1 : σ2 > σ̃2 against the hypothesis H0 : σ. ... 2 = σ̃2. Does the F-test depend on whether µ, µ̃ are known?

19 Jun 2019: Explain how, in general, you would test the hypothesis that one of the componentsof the parameter of interest was zero.

17 Jun 2019: Assuming that a candidate does not retake the test after passing, what isthe mean number of attempts for candidates who passed in 3 or fewer attempts?

19 Jun 2019: 33. (a) Test the hypothesis H0 : π1j = π1 for all j. ... Should you perform formal statistical tests to determine whether there are anydifferences in the characteristics between the two treatment groups?

30 Aug 2019: You may use the comparison test,. provided you state it clearly.].

17 Jun 2019: Carry out an appropriate 5% significance level test, statingyour hypotheses carefully. ... You do not need to derive the test.] What conclusion shouldbe reported to the doctor?

17 Jun 2019: Stating clearly any results you require about the distribution of the maximum-likelihoodestimators of α , β and σ2, explain how to construct a test of the hypothesis that α = 0against an ... The t-test of the null hypothesis that α = 0 against an

17 Jun 2019: f(x; θ) = h(x)g(θ) exp{θt(x)} , x R. Explain in detail how you would test. ... Explain in detail how you would test H0 : ψ = ψ0 against H1 : ψ 6= ψ0, and describethe optimality properties of your test.

30 Aug 2019: Professor Eccentric wishes to test the effect of various types of chocolate bar upon hislecturing speed. ... Part III, Paper 30 [TURN OVER. 10. > anova(lmem1a, lmem2a). Model df AIC BIC logLik Test.

17 Jun 2019: State Wilks’ Theorem on the asymptotic distribution of likelihood-ratio test statis-tics. ... Explain why for large n thelikelihood-ratio test and the t-test are nearly the same.

17 Jun 2019: Find the criticalregion of the most powerful test of size α for the hypotheses H0 : λ = 1 versus H1 : λ = 2.Determine whether or not this test is uniformly most powerful

19 Jun 2019: Consider the hypothesis that the time series y1, y2,. , yT is purely random.Describe the turning point test of this hypothesis.

17 Jun 2019: Use thegeneralised likelihood ratio to obtain a size α test of H0 : θ = 1 against H1 : θ 6= 1. ... x6. Explain how to obtain anapproximate size 0.05 test using the value of T.

30 Aug 2019: 3. 2. Consider the motion of a test particle in the gravitational potential of a binarycomprised of two bodies of mass M1 and M2 M1. ... Part III, Paper 316 [TURN OVER. 4. 3. Consider the evolution of a test particle due to the secular perturbations of

17 Jun 2019: Calculate its value forthe above data. (v) Explain (stating without proof any relevant theory) the rationale for a statisticwhich can be referred to an F distribution to test H0 against the ... What would be theoutcome of a size 0.05 test of H0 with the

30 Aug 2019: Suppose a study is designed to have a test statistic Y with a N(0, 1) distribution under thenull hypothesis that there is no relationship, and the alternative hypothesis is that ... Suppose that n independent studies, each designed with Type I error α

17 Jun 2019: of S3 where a test particle would remain stably at rest?Justify your answer.

17 Jun 2019: 2]. (c) State the comparison test for the convergence of a series of positive terms.

17 Jun 2019: ni=1(Yi α̂ β̂xi)2 are. independent. (b) Find the critical region of the generalised likelihood ratio test of size 5% fortesting H0 : α = 0 versus H1 : α 6= 0. ... Prove that the power function of this test is of theform w(α,β,σ2) = g(α/σ) for

30 Aug 2019: ϕn(x) =1. 2πex. 2/4n, ϕ̂n(λ) =nenλ. 2. 2. Define the space of distributions D′(R) and the corresponding space of test functionsD(R), specifying the notion of convergence

30 Aug 2019: Carry out this test in detail, and give yourconclusion. Compare the models wind2.lm and wind3.lm. ... Explain how to test whether this reduced number of categories of processingmethod is adequate.

17 Jun 2019: 7]. (c) Use the ratio test to discuss the convergence of the non-polynomial solutions on theinterval 1 x 1.

30 Aug 2019: ii) Using (i) above, construct the large-sample likelihood ratio test of.

17 Jun 2019: Paper 1 [TURN OVER. 6. 10F Analysis. State without proof the Integral Comparison Test for the convergence of a series.

30 Aug 2019: For a minimiser u W 1,1((0, 1)2) derive the corresponding Euler-Lagrange equationin the distributional sense over the space of compactly supported test functions.

30 Aug 2019: B1. (euε)ηdx =. B1. ηχ′ε(uε)euεdx (2). for any test function η C0 (B1) (smooth functions with compact support in B1).

17 Jun 2019: Part IA, Paper 1 [TURN OVER. 6. 9F Analysis I. (a) State, without proof, the ratio test for the series.

30 Aug 2019: Explain how D0 and D1 maybe used to test H0 : βk1 =. = βp = 0. Anthers of a particular plant species are prepared under two different storageconditions (1, 2 are control, treatment respectively) ... Interpret these four models. Carry out appropriate

30 Aug 2019: 2. 1 (a) State and prove the Tarski-Vaught test. (b) Let T be a complete theory with a monster model U.

30 Aug 2019: Give a proof orcounterexample. 2. Define the space of test functions D(R) and the space of distributions D′(R),specifying the notion of convergence on each.

30 Aug 2019: The planet may be considered tobehave as a test particle. Show that the equation of the orbit can be cast into the form.

17 Jun 2019: Find a most powerful test of size α of H0 : θ = 0 versus H1 : θ = 1. ... Find a uniformly most powerful test of size α of H0 : θ = 0 versus H1 : θ > 0.

17 Jun 2019: Explain the hypothesis tests, including an approximate test of the fit of H1, thatcan be performed using the output from the following R code. ... If it is, how (according to the conditionalityprinciple) do we test hypotheses on ψ?

30 Aug 2019: Part III, Paper 316 [TURN OVER. 4. 3. (i) Consider a test particle orbiting a star in the same plane as a coplanar system ofN planets. ... Use this to describe, bothquantitatively and with a sketch, the physical space covered by test particles, all of