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18 Feb 2013: Isthe test uniformly most powerful for testing H0 : θ = θ0 against H1 : θ > θ0? ... By first deriving the MLEs under each hypothesis, showthat the likelihood ratio and Pearson’s chi-squared tests are identical to those for theindependence test.

24 Sep 2013: Laboratory, University of Cambridge. 1. Exact Bayesian analysis of a 2 2 contingency table and Fisher’s ‘exact’ signifi-cance test. ... Someone must surely be able to show that these two arespecial cases of a general result, for conditional tests

6 Mar 2013: b) The statistic -3.1 can be used to test for a linear trend in year. ... Explain. (e) The null deviance was 140.42. Construct an appropriate statistic for test-ing a time trend.

26 Feb 2013: SXX/(n1)}1/2. Determine the distribution of T under H0, and hence. determine the size α likelihood ratio test. ... size α likelihood ratio test of equality of means rejects H0 if.

23 Jan 2013: Doesn. 1n log n log log n. converge? 10. Prove the root test, which says the following. ... the series diverges. What happens if a = 1? Add this test to your series grid.

16 Jan 2013: anova(quine.qp1, quine.qp, test="F"). > summary(glm(Days. , poisson, data = quine)). >

10 Oct 2013: To test for linearity of α it is generally best to check α(λ.u µ.v) = λ.α(u) µ.α(v).

24 Jan 2013: Comments and corrections to s.pitts@statslab.cam.ac.uk. 1. Ask your supervisor to test you on the sheet of common distributions handed out inlectures.

23 Sep 2013: from which we could construct a Hotelling’s T2 statistic, of known distribu-tion, to test H0 : µ1 = µ2. ... So we see that the l.r. test of H0 against H1 is to reject H0 in favour of H1iff.

19 Jan 2013: Hint: Use the Weierstrass M-test fromAnalysis II to show that f is locally uniformly convergent.].