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MATHEMATICAL TRIPOS Part IB Tuesday, 4 June, 2019 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2019/paperib_1_2019.pdf17 Jun 2019: a) Find the critical region of the likelihood ratio test of size α in terms of thesample mean X. ... c) Define what it means for a hypothesis test to be uniformly most powerful. -
MATHEMATICAL TRIPOS Part IB Tuesday 1 June 2004 9 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2004/PaperIB_1.pdf17 Jun 2019: 10H Statistics. Use the generalized likelihood-ratio test to derive Student’s t-test for the equalityof the means of two populations. ... You should explain carefully the assumptions underlyingthe test. 11H Markov Chains. -
MATHEMATICAL TRIPOS Part III Thursday 5 June 2003 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2003/Paper41.pdf30 Aug 2019: ii) Describe in detail the Wilcoxon signed rank test, used to test whether acontinuous distribution is symmetric about a point θ0. -
MATHEMATICAL TRIPOS Part III Monday 12 June 2006 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2006/Paper44.pdf30 Aug 2019: Describe how you would construct astratified version of the test. The effect of two treatments, A and B, on the time to a certain event is beingcompared by a log-rank ... test. The individuals are stratified so that there are exactly twoindividuals in -
MATHEMATICAL TRIPOS Part III Friday 1 June 2007 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2007/Paper47.pdf30 Aug 2019: H0 : µ = µ0. (b) Describe briefly how we can modify this test to test hypotheses of the form. ... p 1,. and hence say how to conduct a significance test of hypothesis H0. -
MATHEMATICAL TRIPOS Part II Alternative B Tuesday 4 June ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2002/PaperIIB_2.pdf17 Jun 2019: Find auniformly most powerful size α test of H0 : θ 6 θ0 against H1 : θ > θ0, and find its powerfunction. ... Show that we may construct a different, randomised, size α test with the samepower function for θ > θ0. -
M. PHIL. IN STATISTICAL SCIENCE Friday 3 June, 2005 ...
https://www.maths.cam.ac.uk/postgrad/mphil/files/stats/2005/Paper41.pdf19 Jun 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 = -
MATHEMATICAL TRIPOS Part IB Tuesday 7 June 2005 9 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2005/PaperIB_1.pdf17 Jun 2019: It is desiredto test the hypothesis. H0 : f = f0 against H1 : f = f1,. ... Find the size of the test that minimizes the sum of the error probabilities. -
M. PHIL. IN STATISTICAL SCIENCE Monday 3 June 2002 ...
https://www.maths.cam.ac.uk/postgrad/mphil/files/stats/2002/Paper39.pdf19 Jun 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) = -
MATHEMATICAL TRIPOS Part IB Thursday, 7 June, 2012 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2012/PaperIB_3.pdf17 Jun 2019: Given θ0 6= 20. we wish to test H0 : θ = θ0 against H1 : θ = 20. ... Let φ(θ0) be the test which accepts H0 ifand only if X A(θ0), where. -
MATHEMATICAL TRIPOS Part IA Thursday 30 May 2002 9.00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2002/PaperIA_1.pdf17 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. -
MATHEMATICAL TRIPOS Part III Thursday, 7 June, 2012 1:30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2012/paper_41.pdf30 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. -
MATHEMATICAL TRIPOS Part III Thursday 6 June 2002 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2002/Paper46.pdf30 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 -
MATHEMATICAL TRIPOS Part III Thursday, 2 June, 2011 1:30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2011/paper_32.pdf30 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 -
MATHEMATICAL TRIPOS Part III Friday, 3 June, 2011 1:30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2011/paper_31.pdf30 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. -
MATHEMATICAL TRIPOS Part III Thursday, 3 June, 2010 9:00 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2010/Paper61.pdf30 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 -
MATHEMATICAL TRIPOS Part IA Thursday 29 May 2008 9.00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2008/PaperIA_1.pdf21 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.]. -
MATHEMATICAL TRIPOS Part IB Friday 7 June 2002 1.30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2002/PaperIB_4.pdf17 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. -
M. PHIL. IN STATISTICAL SCIENCE 9 am Monday 11 ...
https://www.maths.cam.ac.uk/postgrad/mphil/files/stats/2001/Paper101.pdf19 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 -
MATHEMATICAL TRIPOS Part III Friday 6 June 2008 9.00 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2008/Paper46.pdf30 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
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