NONPARAMETRIC METHODS — DU B.Sc (hons) Statistics Previous Year Question Papers

a. Answer the following questions: (i) Discuss at least two situations where non-parametric methods are preferred over parametric ones. (ii) Differentiate between nominal and ordinal scales of measurement along with suitable examples. (iii) Explain the two advantages ofnon-parametric over parametric method. (iv) Write first two moments of the null distribution of the number of runs r, for two independent samples of sizrs m and n. (v) ln case of signed rank test wha{ do we do with the pairs with same magnilude? b. Fill in the blanks: (i) A parametric test assumes that the underlying population distribution is (ii) The most common mqrsure of central tendency used in non-parametric tests is the (iii) Non-parametric tests are also called specifi c popularion distribution. tests because llrey do not assume a (iv) Relation between two values of U statistic is (v) The measurement scale used in case ofAutomobile License plates is Define empirical distribution function. Let dam set { l, 2,5, 7. 8} and rhen (i) find the empirical distribution F,(0), F"(2), F"(2.5), F"(5), F,(7.2) and F"(9). (ii) define quantiles and find the quantile distribution eo.zs,eso, and e0.7s for the above data s€t. (b) Explain steps involved in wald-wolfowitz run test for two samples. The weights (in grams) of seeds from two batches are given below: Test at a:0.05 whether the two samples come from the same population. [Zo os = I .96 and 3 (a) Distinguish between parametric and non-parametric tests. (b) Descdbe the sign test for testing that the popularion median is Mo against the altemative thal the median is Mr(> Mo). The brcaking strength (in pounds) of a random sample of I0 ropes made by a manufacturer is given by 163, 165, 165, 160, l7t, t58, tsl,162,,t69, l7Z. Use sign test to test the manufacturer's claim that the average breaking strength of a rope is greater than 160 pounds at 5olo level of significance.fN rc. c c5 .= 8, Nr,oos = 8l (7, S) 4 (a) Describe Wilcoxon Signed-Rank Test for a two-sample problem. The following data represent the differences in blood pressure (before and after treatment) for 8 patients:-z, 3, 4, -L, 5, -3, 6, Z; Using the Wilcoxon Signed-Rank Test" tesr whether the rearment has a srgniticant effecl on blood pressure ed a = 0.05. (b) Describe the Mann-Whitney-Wilcoxon U-test and obtain the mean and variance of the test statistic U. How is the test carried out for large samples? The following data represents lifetime (in hours) of batteries for 2 different brands A and B Examine the average life of 2 brands is same at 5% level of significance. 5 (a) Explain the meaning and importance of testing randomness in a sequence. Also state the conditions under which the test is applicable. (b) Discuss a non-parametric test analogous to one-way analysis of variance for testing that k-independent sample are drawn from different populations. Given the following data for four independent groups: