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30 Aug 2019: At the end of the experiment, all subjectswere again given the approach test. ... For hypothesis tests, state the null hypothesis, the result of the test andyour conclusion.

30 Aug 2019: A dentist wants to test a new method of filling teeth (Method B) against thestandard method (Method A). ... a) Comment briefly on whether the log-rank test captures all the relevantevidence in the study.

17 Jun 2019: State the alternatingseries test and prove it from the fundamental axiom. ... You may use any test for convergence provided you state it correctly.

17 Jun 2019: x2. a2+. y2. b2+. z2. c2= 1. 3H Statistics. From each of 100 concrete mixes six sample blocks were taken and subjected tostrength tests, the number out of the six blocks ... No. x failing strength tests 0 1 2 3 4 5 6No.

30 Aug 2019: Define the likelihoodratio test statistic Λn for this testing problem, and express it in terms of the maximumlikelihood estimator θ̂n. ... Define further the score statistic and the score test. How would you choose criticalvalues for the rejection

30 Aug 2019: 2. 1. Consider a test particle orbiting a binary comprised of a star and planet of massesM and Mpl. ... ẋ′ = ẋ µα0.5(1 e2)0.5A sin nplt ,. ẏ′ = ẏ µα0.5(1 e2)0.5A cos nplt ,where µ =. MplM Mpl. and α =apla. Even though the test

30 Aug 2019: Show that infinitesimal changes in the specific energyand specific angular momentum vector of a test particle, within the family of circularorbits, are related by. ... Two test particles are constrained to move on circular orbits in a spherically

21 Aug 2019: Paper 1. 3. 3F Analysis I. State the ratio test for the convergence of a series. ... tests for convergence, provided that they are clearly stated.].

17 Jun 2019: It is desired to test the hypothesis H0 : θ 0 against thealternative H1 : θ > 0. ... Show that there is a uniformly most powerful test of size α = 1/20and identify a critical region for such a test in the case n = 9.

30 Aug 2019: Between 2003 and 2007,the annual number of cocaine positives in Monday tests increased from 250 to 500.In 2007, 30% of the Monday cocaine-positive tests gave a maximum ... Could one construct a 5%-level test with 80% power, todetect statistically whether

19 Jun 2019: i) Write down clearly an appropriate model for the above design, and analyse it carefully.Test whether there is a difference between the 6 varieties. ... Interpret the results and test any assumptions (graphically and/or otherwise) made.Give possible

19 Jun 2019: Test the hypothesisthat premiums are not affected by the first two speeding convictions. ... i) Summarise the data using appropriate plots and tables. [3]. (ii) Use nonparametric methods to test whether or not the MRSA rates have changed.

17 Jun 2019: For 0 < α < 1, derive the test that is most powerful among all tests of size atmost α. ... Obtain an expression for the power of your test in terms of the standard normaldistribution function Φ().

30 Aug 2019: library(MASS)> stepAIC(model1.lm,. scope = list(upper = wind maxtemp insol, lower=1), test="F"). ... Analysis 1:. > melanoma1.glm <- glm(propcases age city, binomial, weights = pop)> anova(melanoma1.glm, test="Chisq").

30 Aug 2019: 2) Briefly explain the difference between the goals of a classical Sequential ProbabilityRatio Test and a CUSUM plot. ... iv) Write down tables with the observed and expected counts if association istested at the chromosome (haplotype) level instead of

24 Sep 2019: test, the first task of which is to prove that all odd number are prime. ... Nowadays, the examinations are much more friendly, being de-signed to test your knowledge of the courses you have attended ratherthan your ability to jump through mathematical

30 Aug 2019: Consider the case of a test particle orbiting very close to a planet with mass M.Let the gravitational potential consist of a monopole term and a quadrupole describingthe planet’s ... Find the radial and vertical frequencies of motion. Show that thethe

16 Aug 2019: To test this enter. >> amatrix=printsquares(1,10);. >> amatrix. Note that we have used amatrix as the name of the matrix in which to store the output fromthe function printsquares; we ... 4.4 Exercises. 1. Test your function printsquares with m60 and m>n,

17 Jun 2019: What are the hypothesis tests corresponding to the final column of the coefficientstable? ... What is the hypothesis test corresponding to the final line of the output?

30 Aug 2019: EPR pairs to serve as check bits to test for Eve’s. ... announces this fact.5: Alice selects n of the 2n encoded EPR pairs to serve as check bits to test for Eve’s.

17 Jun 2019: As a test signal, the radio station chooses a single pulse given by. ... 6]. (c) Use the ratio test to determine the radius of convergence of each series.

30 Aug 2019: Transmitted allele Untransmitted allele. 1 21 a b2 c d. ii) Calculate the value of transmission disequilibrium test (TDT) from this table. ... Marker allele Transmitted Untransmitted. 1 w y2 x z. and use the data in the cells of this table to calculate

17 Jun 2019: 12D Statistics. What is meant by a generalized likelihood ratio test? ... Explain in detail how toperform such a test. Let X1,. ,Xn be independent random variables, and let Xi have a Poissondistribution with unknown mean λi, i = 1,.

17 Jun 2019: Derive the form of the size-α generalizedlikelihood-ratio test of the hypothesis H0 : µ = µ0 against H1 : µ 6= µ0, and show that itis equivalent to the standard t-test ... You should state, but need not derive, the distribution of the test statistic.

17 Jun 2019: limx0. AeA/x2. BeB/x2. eA/x2 eB/x2. [3]. (c) State the ratio test for determining convergence properties of series. ... 2]. State what, if anything, the ratio test tells you about the convergence or divergenceof the following series:.

30 Aug 2019: State any theorem that you use. (c) Fix δ (0,1). Using the statistic C = max16j6d cj, give a test ψ such thatwhenever. ... Using the statistic Λ = maxSS u(S)Σ̂u(S),give a test ψ such that for some constant C > 0, whenever.

30 Aug 2019: Xn, howwould you perform such a test of size α? ... Write down the test statistic and thecritical region. [Derivation of the test statistic’s asymptotic distribution is not required here.].

30 Aug 2019: Describe how this asymptotic result is related to the Wald test of H0 : θ = θ0against H1 : θ 6= θ0. ... Describethe Wald test of H0 : ψ = ψ0 against H1 : ψ 6= ψ0.

19 Jun 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: Show that the test with critical region {(x1, x2, x3) :. 3i=1 xi > 5} is a likelihood. ratio test of H0 against H1. ... What is the size of this test? Write down an expression forits power.

30 Aug 2019: Carryout a formal hypothesis test to determine whether blow3.glm is an improvement overblow2.glm. ... traffic2.glm <- glm(naccoffset(log(years))LocBefaft,poisson). > anova(traffic2.glm,test="Chisq"). Df Deviance Resid. Df Resid.

30 Aug 2019: Number of Fisher Scoring Iterations: 3. >fisher.test(rbind(a,b)). Fisher’s exact test. data: rbind(a, b). ... The reported variables are. npreg = number of pregnancies,glu = plasma glucose concentration in an oral glucose tolerance test,bp = diastolic

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

30 Aug 2019: 0. (i) Show that the angular velocity (r), epicyclic oscillation frequency κ(r) and verticaloscillation frequency z(r) associated with circular test-particle orbits in the mid-planeare given by. ... where a represents the radius of the black hole. Find

19 Jun 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

17 Jun 2019: tests performed under the summary and anova commands. > fit1 <- lm(xab). >

30 Aug 2019: Neyman. allocation) is: R =. p0(1p0)p1(1p1). Note: the Z-test (Wald Test) is is based on a statistic Z = p̂0p̂1σ2p̂. ... After the 10thpatient’s outcome is assessed a statistical test is done at a 10% significance leveland shows no significant

30 Aug 2019: c) Show how to test for a difference between the direct and indirect evidence re-garding the comparison of warfarin and aspirin. ... ii) Suppose we test 10 biomarkers for association with bowel cancer, and de-clare significance according to a p-value

17 Jun 2019: What arethe size and power of the test in terms of α and β? ... Is it admissibleas a test of H0 against H1? Paper 2 [TURN OVER.

17 Jun 2019: Derive carefully a (generalized) likelihood ratio test of independence of classifica-tion. ... What is the result of applying this test at the 0.01 level? [

17 Jun 2019: Find the best test of size α, 0 < α < 1, of the hypothesisH0 : θ = θ0 against H1 : θ = θ1, where θ1 > θ0. ... When α = 0.05, for which values of θ0 and θ1 will the power of the best test be atleast 0.95?

17 Jun 2019: Conduct a goodness-of-fit test at the 0.05 level for the null hypothesis that the coins areall fair. ... Prove that f is continuous on E. State the Weierstrass M-test for uniform convergence of a series.

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.

16 Oct 2019: Hence, approximate the distribution of the generalisedPearson statistic, and conclude whether there is evidence of overdispersion in a test withsignificance level 5% approximately. ... d) Can we expect to be able to use the usual deviance-based test for

17 Jun 2019: Define the terms size and power for a test of onesimple hypothesis against another. ... x|/2,x R. Find the test of size α,α < 14 , which maximises power, and show that the power is et/2,.

19 Jun 2019: Using the results of (i) above, show that the generalizedlikelihood ratio test of.

19 Jun 2019: Xβ = X1β1 X2β2,. where X is partitioned as (X1 : X2), and β is similarly partitioned as β =(. β1β2. ). How would you test the hypothesis ω : β = 0 against? ... How would you test thehypothesis ω1 : β1 = 0 against?

30 Aug 2019: Consider the following (edited)R output. > model1<-glm(purchasepricelayout,family="binomial"). > model2<-glm(purchaseprice,family="binomial"). > anova(model1,test="Chisq"). ## ... Which model is preferable? Describe thehypothesis test that has been

30 Aug 2019: An experiment was carried out to investigate operators of a certain type ofhydrostatic testing machine used to test the water repellency of fabrics. ... Now test for an operator effect. [ F4,3 (0.05) = 9.12 F3,6(0.05) = 4.76 F6,3(0.05) = 6.16F3,15(0.05) =

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 =