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17 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.

30 Aug 2019: The bank tests authenticityby measuring the projection onto the relevant qubit. ... Show that there is a positive numberp0 such that, whatever his strategy, the probability of at least one of the N banknotesfailing the bank’s authenticity test is

30 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

30 Aug 2019: bomb is dud or live, the test is repeated. ... Show that, by choosing U,U′ appropriately and repeating the test appropriately, theprobability of identifying a live bomb without detonating it can be increased to arbitrarilyclose to 1/2 within this

17 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.

17 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.

30 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.

30 Aug 2019: ii) Describe in detail the Wilcoxon signed rank test, used to test whether acontinuous distribution is symmetric about a point θ0.

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.

19 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 =

19 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) =

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

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.].

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

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