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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 =

17 Jun 2019: i) Find (with careful justification) the form of the size-α likelihood–ratio test of thenull hypothesis H0 : µY = 0 against alternative H1 : (µX,µY ) unrestricted. ... ii) Find the form of the size-α likelihood–ratio test of the hypothesis.