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21 Jan 2011: bndivergent. 9. (Abel’s test.) Let an and bn be two sequences and let Sn =n. ... Deduce the alternating series test. Does the series. n=1cos(n). n converge or diverge?

16 Feb 2011: 7. Let X1,. , Xniid Exp(θ). Find the likelihood ratio test of size α of H0 : θ = θ0 against. ... Is the test uniformlymost powerful for testing H0 : θ = θ0 against H1 : θ > θ0?

21 Nov 2011: Emphasise has contractedthe Macguffin virus. A test is available that will detect the virus at any dilution. ... Write downthe exact form of the test when there are 2n crew members and pi = 2.

21 Jan 2011: bndivergent. 9. (Abel’s test.) Let an and bn be two sequences and let Sn =n. ... Deduce the alternating series test. Does the series. n=1cos(n). n converge or diverge?

11 Feb 2011: Xniid N (θ, σ2), and we wish to test H0 : θ = 0 against the. ... one-sided alternative H1 : θ > 0. Write a simulation to plot the power functions ofthe t-tests when n = 20 and σ = 0.5, 1, 2 (power.t.test may help).

14 Mar 2011: Do they still fit the data satisfactorily? Furthermore,perform a likelihood ratio test of the reduced model with 2 age categories against themodel with 3 age categories. ... This can be done using the anova command by specify-ing that you’re performing

6 Oct 2011: To test for linearity of α it is generally best to check α(λ.u µ.v) = λ.α(u) µ.α(v).

1 Feb 2011: 1. Ask your supervisor to test you on the sheet of common distributions handed out inlectures.

9 Mar 2011: ratio test of equality of means rejects H0 if. F 1.

16 Mar 2011: where Yi Poisson(µi). Compare the data with the fitted values from the new model.Test for the significance of the interaction term. ... To see this, apply the anova function with test=‘F’. Recall that whentesting model M1 against M2, where M1 M2

1 Mar 2011: In each case, explain how would you test these hypotheses, assuming that thefitted values in each cell are not too small.

2 Feb 2011: How would you perform the hypothesis test?[Hint: from the first example sheet rank(P ) = p, and rank(I P ) = n p.Similar arguments give that rank(P0) = p0.

18 Oct 2011: 15. (Abel’s test) Let an and bn be real-valued functions on E R.

25 Feb 2011: models and used an ANOVA test to conclude a preferencefor the one that included a quadratic term.

18 Oct 2011: 15. (Abel’s test) Let an and bn be real-valued functions on E R.

4 Mar 2011: How can you perform this test with a single R com-mand?