Semester - IV Model paper - I

                 SECTION- A

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

1.    Define Null and Alternative hypothesis.

2.    Write a short note on randomized and non randomized test functions.

3.    Define Type I and Type II errors.

4.    Define sample proportion and population proportion. Write test statistic for single  and difference of proportions.

5.    Explain large sample test procedure for difference of standard deviations.

6.    Explain small sample test procedure for single mean.

7.    Define Nominal and Ratio scales.

8.    Write differences between parametric and non parametric methods.

SECTION –B

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

9(a). Define Most powerful test. State Neyman-Pearson Lemma. Obtain the most powerful   
         test for testing the mean µ = µ₀ against µ = µ₁ (µ > µ_0, µ < µ₀) where σ² = 1 in normal
         population.       

                                                                       (OR)

  (b). In township, the milk consumption of the families is assumed to be exponentially 
         distributed with the parameter . The hypothesis H₀: =5 is rejected in favour of
         H₁: =10 if a family selected at random consumes 15 units of milk or more. Obtain

         the critical region and size of the errors.

10(a).(i). Derive the large sample test procedure for difference of means.

         (ii). Define order statistics and state their distributions.

                                                                        (OR)

    (b). Describe the test procedure for Fisher’s Z transformation for difference of
           correlation coefficients. In a large consignment of oranges, a random sample of 64   
           oranges revealed that 14 oranges were bad it reasonable to assume that 20% of the
           oranges were bad test at 1% level.

11(a). Stating the condition of validity of chi-square test and explain chi-square test for testing
           independence of attributes.              

                                                                        (OR)

    (b)(i). Explain small sample test procedure for equality of population variances.

        (ii). Two types of drugs were used on 5 and 7 patients reducing their weight. Drug A
               was imported and drug B was indigenous. The decrease in the weight after using
               the drug for 6 months was as follows.

Drug A	10	12	13	11	14
Drug B	8	9	12	14	15	10	9

12(a)(i). What is meant by non-parametric methods? State their advantages and
              disadvantages.

        (ii). Explain sign test.

                                                                      (OR)

    (b)(i). Define Run and explain Wald-Wolfowitz’s run test.

        (ii). Explain Test for randomness for single sample.