IGNOU MST 21 SOLVED ASSIGNMENT

Included:

MST 021 (January 2025 - July 2025) - ENGLISH

TUTOR MARKED ASSIGNMENT

MST-021: Classical and Bayesian Inference

Course Code: MST-021

Assignment Code: MST-021/TMA/2025

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1(a) State whether the following statements are True or False. Give reasons in support of your answer:

(i) If the form of the population is not known and data are in ordinal form then we apply the Wilcoxon Signed rank test for testing hypothesis about average.

(ii) The Neyman-Pearson lemma provides the most powerful test of size a for testing a simple hypothesis against a simple alternative hypothesis.

(iii) The Rao-Blackwell theorem enables us to obtain a manimum variance unbiased estimator through complete statistic.

(iv) For testing goodness of fit when the data are in categorical form, we use K-S test.

(v) In the Bayesian approach, we treat the parameter as a constant.

(b) Differentiate between Rao-Blackwell and Lehmann-Scheffe theorems.

2. A faculty member of a university receives a number of emails. If X represents the number of spam emails in n emails and follows a binomial distribution with parameters  where  is the probability of getting spam email, then find the posterior distribution of considering the following beta distribution.

Also, find the posterior mean of θ .

3. A food processing company packages 10 gm of honey in small jars. Previous experience suggests that the volume of a randomly selected jar of the company’s honey is normally distributed with a known variance of 2 gm. Drive likelihood ratio test for testing

at a α level of significance. Given

4. If the number of weekly accidents occurring on a mile stretch of a particular road follows a Poisson distribution with parameter λ . Then

(i) Find the Cramer-Rao lower bound for the variance.

(ii) Also, find the UMVUE of λ .

5. The following data give the sales of 6 models of mobiles at four different stores. The sales of each mobile (in number of mobiles sold) from each store are given as follows:

Store A	Store B	Store C	Store D
58	74	35	78
55	57	51	85
38	65	41	62
63	48	52	75
41	83	54	87
50	61	53	57

 

Test whether there is a significant difference in the sales of the four stores by using the Kruskal Wallies test at 1% level of significance 

 

MST 021 (January 2026 - July 2026) - ENGLISH

Course Code: MST-021

Assignment Code: MST-021/TMA/2026

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are True or False. Give reasons in support of your answer:

(5×2=10)

(i) When the population distribution is unknown and the data are measured on a nominal scale, the Sign test can be used to test a hypothesis about the median.

(ii) In the Bayesian framework, prior information about the parameter is combined with the likelihood to obtain the posterior distribution.

(iii) The Wilcoxon rank-sum test is a non-parametric alternative to the two-sample t-test when normality is not assumed.

(iv) A complete sufficient statistic guarantees the uniqueness of the unbiased estimator obtained through it.

(v) The power of a statistical test is the probability of accepting the null hypothesis when it is true.

2. A pharmaceutical company fills medicine bottles with a target weight of 500 mg. It is known that the filling weights are normally distributed with known variance o² = 16. Derive the likelihood ratio test for testing

Ηο: μ = 500againstH₁: μ ≠ 500

at significance level a.

3. Suppose the number of breakdowns per month in a factory follows a Poisson distribution with parameter λ.

(i) Find the Cramer-Rao lower bound for an unbiased estimator of λ.

(ii) Obtain the UMVUE of λ.

(i) Find the Cramer-Rao lower bound for the variance. (ii) Also, find the UMVUE of $lambda$. (20)

5. Two independent groups of patients were given Drug X and Drug Y. The recovery times (in days) are as follows:

Drug X	8	10	9	7	11
Drug Y	6	7	5	8	6

(i) State the null and alternative hypotheses.

(ii) Explain why the Mann–Whitney U test is appropriate for this data.

(iii) Perform the test at the 5% level of significance and draw a conclusion. (20)

6. Differentiate between classical and Bayesian estimation. (10)

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