Statistical Inference Modal Paper

 

GAYATRI VIDY PARISHAD COLLEGE FOR DEGREE AND PG COURSES (AUTONOMUS).

B.Sc. third semester ( Statistics)

Paper -III Statistical Inference (Model paper)

Date:                                                                                                               Max.Marks:75.

Time:3 hours.

Section-A.

Answer the following questions.                                                                  5x10=50.

1(a). Define Chi-Square distribution. Give any five properties of this distribution also give its       applications. (CO1).

Or

1(b). Define the following  (CO1)

(i)                 Parameter.

(ii)               Statistic.

(iii)             Sampling Distribution.

(iv)             Standard Error.

2(a). Show that sample mean is always an unbiased estimator of the population mean. While sample variance is not an unbiased estimator of population variance.  (CO2)

Or

2(b) If X follows a normal distribution with mean 𝜇 and variance σ² obtain the maximum likely hood estimators of the population parameters. (CO2)

3(a). State and prove Neyman-Pearson’s lemma. (CO3)

Or

3(b) If X follows a normal distribution with mean θ and variance one obtain the best critical region of size α for testing the simple null hypothesis H₀:θ=θ₀ against the alternative H₁:θ=θ₁ (θ₁>θ₀ ). (CO3).

4(a). Explain large sample test for testing the equality of standard deviations of two normal populations. (CO4)

Or

4(b) Obtain the 95% confidence interval for the mean of a normal distribution when the population variance is not known. (CO4)

5(a). What are the assumptions made in non-parametric tests? Give the merits and demerits of non-parametric tests. (CO5)

Or

5(b). Explain run test for testing the randomness of the given data. (CO5)

Section-B.

Answer any five of the following.                                                                3x5=15.

6) Define almost sure convergence of a sequence of random variables. (CO1)

7)State Fisher-Neyman factorization theorem. (CO2).

8) Explain the two types  of errors in testing of a statistical hypothesis. (CO3)

9) Explain small sample test for correlation coefficient. (CO4)

10) Write about the different scales of measurement. (CO5)

11) Define F distribution. What can you say about its mode? (CO1)

12) When will you say an estimator is consistent? (CO2)

13) What do you understand by size of the test function? (CO3)

Section-C

Answer all the questions.                                                                  2x5=10.

14) Give the relation between ‘t’ and ‘F’ distributions. (CO1).

15) When will you say an estimator is accurate? (CO2)

16) Define a statistical hypothesis. (CO3)

17) What is a confidence interval? (CO4)

18) Give the variance of  run statistic in the case of large samples.(CO5)