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  2. UNIVERSITY OF CAMBRIDGE Faculty of Mathematics SCHEDULES OF LECTURE…

    www.statslab.cam.ac.uk/~lab85/resources/schedules1819.pdf
    2 May 2023: Comparison and ratio tests, alternating series test. [6]. ContinuityContinuity of real- and complex-valued functions defined on subsets of R and C.
  3. 42 Paper 1, Section I 7H StatisticsDescribe the generalised ...

    www.statslab.cam.ac.uk/~lab85/resources/Stats2012.pdf
    28 Apr 2023: It is desired to test the hypothesis H0 : λ = µ against H1 : λ 6= µ. ... Let w(θ) denote the power function of this test at θ (> 1).
  4. 48 Paper 1, Section I7H Statistics What does it ...

    www.statslab.cam.ac.uk/~lab85/resources/Stats2009.pdf
    28 Apr 2023: What is the critical region C of a test of the null hypothesis H0 : θ Θ0 against. ... the alternative H1 : θ Θ1? What is the size of a test with critical region C?
  5. 41 Paper 1, Section I 7H StatisticsLet x1, . ...

    www.statslab.cam.ac.uk/~lab85/resources/Stats2013.pdf
    28 Apr 2023: It. is desired to test H0 : f(x) = 1 against H1 : f(x) = 2x. ... Let δ : [0, 1] {0, 1} define a test by δ(x1) = i ‘accept Hi’.
  6. 39 Paper 1, Section I6H Statistics State the Rao-Blackwell ...

    www.statslab.cam.ac.uk/~lab85/resources/Stats2022.pdf
    27 Apr 2023: d) Describe a test of size α for the null hypothesis H0 : σ21 = σ. ... Suppose thereexists a likelihood ratio test of size α for H0 against H1.
  7. 25 1/I/3D Statistics Let X1, . . . ,Xn ...

    www.statslab.cam.ac.uk/~lab85/resources/Stats2001.pdf
    28 Apr 2023: Define the terms size and power for a test of onesimple hypothesis against another. ... Part IB. 26. 2/II/12D Statistics. What is meant by a generalized likelihood ratio test?
  8. UNIVERSITY OF CAMBRIDGE Faculty of Mathematics SCHEDULES OF LECTURE…

    www.statslab.cam.ac.uk/~lab85/resources/schedules2021.pdf
    2 May 2023: Comparison and ratio tests, alternating series test. [6]. ContinuityContinuity of real- and complex-valued functions defined on subsets of R and C.
  9. 46 A1/12 B1/15 Principles of Statistics (i) A public ...

    www.statslab.cam.ac.uk/~lab85/resources/PoS2003.pdf
    28 Apr 2023: How might the parametric bootstrapbe used to obtain a test of H0 of exact size α? ... Your account should include a discussion of natural statistics andtheir properties and of various conditional tests on natural parameters.
  10. 29 1/I/7C Statistics A random sample X1, . . ...

    www.statslab.cam.ac.uk/~lab85/resources/Stats2006.pdf
    28 Apr 2023: 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.
  11. 45 Paper 1, Section I 7H StatisticsLet X1, . ...

    www.statslab.cam.ac.uk/~lab85/resources/Stats2016.pdf
    28 Apr 2023: Find the criticalregion of the most powerful test of size α for the hypotheses H0 : λ = 1 versus H1 : λ = 2.Determine whether or not this test is uniformly most powerful ... Prove that the power function of this test is of theform w(α,β,σ2) =

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