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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

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: 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

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.

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: 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.