147 terminal exercises 1 what is the basis for the

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14.7. TERMINAL EXERCISES 1) What is the basis for the use of term sign test ? 2) Define a run in a sequence of symbols. 3) What indication can one get from the number of runs ? 4) In what way the ordinary sign test can be used for paired samples ? Objective type questions 1) Ordinary sign test utilizes a) Poisson distribution b) Binomial distribution c) Both (a) and (b) d) Neither (a) nor (b) 2) If there are zero differences in sign test, they may be a) Discarded b) Treated half of them as positive c) Treated half of them as negative d) All the above 3) A sequence of symbols shows lacks of randomness if there are a. Too many runs b. Two few runs c. Both (a) and (b) d. Neither (a) nor (b) 4) If there are 10 symbols of two types, equal in number, the maximum possible number of runs is a. 8 b. 9 c. 10 d. None of the above 14.8. SUPPLEMENTARY MATERIALS 1) 2)
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121 3) 4) 14.9. ASSIGNMENTS 1) Use the sign test to see if there is a difference between the number of days required to collect an account receivable before and after a new collection policy. Use the 0.05 significance level. Before : 33 36 41 32 39 47 34 29 32 34 40 42 After : 35 29 38 34 37 47 36 32 30 34 41 38 2) A sequence of small glass sculptures was inspected for shipping damage. The sequence of acceptable and damaged pieces was follows D,A,A,A,A,D,D,D,D,D,A,A,D,D,A,A,A,A,D,A,A,D,D,D,D Test for the randomness of the damage to the shipment using 0.05 significance level. 3) Given the following Ten paired sample observations X 42.7 50.4 44.2 49.7 49.4 55.3 46.1 49.8 48.7 45.9 Y 54.2 43.7 34.0 46.1 55.4 58.2 53.4 43.6 57.0 61.9 Test the hypotheses that the two samples have come from identical population by using sign test. 4) On testing a coin 15 times, the following sequence of heads (H) and tails (T) was obtained TT HHH T H T HHH TT HH Test whether the coin is unbiased by the Run test. 14.10. REFERENCE BOOKS 1) Agarwal, B.L., ‘Basic Statistics’, Wiley Eastern Ltd, New Delhi, 2 nd ed., 1991 2) Gibbon. JD., “Non -Parametric Statistical Inference ” Mc Graw Hill Kogakusha Ltd, Tokyo. 3) S.C. Gupta and V.K. Kapoor “Fundamental of Mathematical Statistics , Sultan Chand & Sons. 14.11. LEARNING ACTIVITIES Non-parametric tests are very convenient when the real world presents distribution-free data on which a decision must be taken. But the sign test is just another applications of the familiar normal approximation to the binomial using + and instead of success and failure. Run tests can often be useful in quality management situations where we are trying to separate out systematic variation from random variation. Systematic variation can cause the kinds of patterns that runs tests detect. 14.12. KEY WORDS 1) Paired data 2) Randomness 3) Identical occurrences 4) Theory of runs 5) Continuous variable.
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122 LESSON 15 RANK SUM TESTS 15.1. INTRODUCTION In the analysis of variance to test the hypothesis that several population means are equal. We assumed in such tests that the populations were normally distributed with equal variances. Many times these assumptions cannot be met and
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