Semester IV, Model Paper 2


Subject: STATISTICS, Paper-IV: Inference
Time: 3 hrs                                                                                                    Max. Marks: 80
                                                                 SECTION- A       

I. Answer any Five questions:                                                                                  5*4=20M

1.    Define types of errors.
2.    Write a short note on randomized and non randomized test functions.
3.    Define level of significance, power of the test.
4.    Explain clearly the procedure generally followed in testing of a hypothesis.
5.    Explain test for randomness.
6.    Explain large sample test procedure for single proportion.
7.    Define interval and ratio scale.
8.    What is meant by non parametric methods.

SECTION –B
 II. Answer all questions:                                                                                          4*15=60M

9(a). State Neyman-Pearson Lemma. Obtain the best critical region of size α for testing Ho: λ = λo  vs H1: λ = λ1 (< λo) based on sample size n from Poisson distribution.                                                                                                                                (OR)
   (b). If X≥1 is the critical region for testing Ho: Ө=2 vs H1: Ө=1 on the basis of single observation from the exponential distribution, obtain the probabilities of type I and II errors. Also power of the test. 

 10(a).(i). Explain the large sample test procedure for difference of standard deviations.
         (ii). Define order statistics and state their distributions.
                                                                        (OR)
    (b). Explain large sample test procedure for testing the significance of single mean. A sample of 900 members has mean 3.4cm. Is the sample drawn from the population with mean 3.25cm and standard deviation 2.61cm. Also find 95% confidence limits.

 11(a). Stating the conditions of validity of chi-square test, explain chi-square test for goodness of fit.
                                                                                    (OR)
     (b). Explain small sample test procedure for testing the significance difference between the means for independent and related samples.

12(a). Distinguish between parametric and non parametric methods. Explain Mann-Whitney U-test
                                                                        (OR)
    (b). Explain non parametric test procedure for testing the equality of Medians.
                                                                       

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