Introduction to Non-Parametric Methods — DU B.A. (Prog.) with Statistics as Major Discipline Previous Year Question Papers

2373570008 (NEP-UGCF) Introduction to Non-Parametric Methods (DSE) All necessary critical values are provided at the end of each numerical part. a). The following 7 observations are obtained: 4, 9, 15, 22, 28, 35, 43. Test at the 5% level whether these come from a Uniform distribution on [0, 50]. •`[dit.ical Value: D(0.05, n=7) = 0.483] 2. (a) .Explain the Sign Test for.testing the median of a population. What are .the advantages of the Sign'rfe.;t over parametric alternatives? (b). The weekly expenses (in € hundreds) 9f 11 families are: 32, 45, 28, 51, 37, 40, 55, 33, 47, 30, 42. Test at the 5% level whether the median weekly expense is €3800 (i.e., 38 hundreds). [Critical Value: For n = 11. two~talled at a = 0.05, reject Ho if irin(S+, S~) <_`1] 3.(aj.DefinetheSpearmanRank-OrderCorrelationCoefficientandwhteitsformula.Explainthe step,by-step procedure for computing it. What does the value of the coefficient indicate about the relationship between two `variables? Discuss the assumptions required and the `level of measurement needed for this test. (b) Ten students are ranked by two examiners...in a viva-voce examination as follows: Compute the Spearman Rank Correlation Coefficient and test its significance at the 5% level. [Critical Valrie: rs(0.05, n=IO, two-talled) = 0.648] 4. (a). Explain the Median Test for comparing two independent samples. Why is the Chi-Square test with Yates' cori.ection used when the sample sizes are small? What are the limitations of the Median Test compared to the .Mann-Whitney U Test? (b) Two groups of students scored the following marks in an aptitude test: Using the Median Test, test at the 5% level whether the two groups have the same median. [Critical Value: x°(0.05, 1) = 3.841] 5. (a). Describé the Mann-Whitney 'U Test. State the formula for the normal approximation. (b) The reaction times (in milliseconds) for two groups of subjects are: Test at the 5% level whether the two groups differ in median reaction time. [Critical Value: U(0.05, ni=5, nz=6, two-tailed) = 5] 6. (a) Describe the Kruskal-Wallis one way analysis of variance rank test: (b) Three groups of patients receive different treatments and their recovery times (in days) are: * Test at the 5% level whether the treatments have different median recovery times. [Critical Value: x°(0.05, 2) = 5.991J 7.(a) Define the Chi-Square Goodness of Fit test. Explain the difference between a one-tailed and two-tailed application of this test. Why is the Chi-Square Goodness of Fit test always right-tailed?. (b) A survey of 100 people on their preferred season gives: Spring SummerT Autumn Tw Winter Test at the 5% level whether the preferences are equally distributed across the four seasons. [Critical Value: x°(0.05, 3) = 7.815] 8.(a) Describe the One-Sample Runs Test. Explain how this test can be used to test the randomness of a sample. (b) The signs of residuals from a fitted regression model, in order, are: