IGNOU MSCAST MST 16 Statistical Inference Solved Assignment ENGLISH

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MST 016 (January 2026 - July 2026) - ENGLISH

MS 116: Statistical Inference

Course Code: MST-016

Assignment Code: MST-016/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:

(i) The mean square error is calculated when the estimator is unbiased.

(ii) If the sample size tends to infinity, the variance of a consistent estimator must tend to zero.

(iii) In the method of moments, population moments are equated to corresponding sample moments.

(iv) A 95% confidence interval is smaller than a 99% confidence interval.

(v) The chi-square distribution is symmetric for all degrees of freedom.

2. A school caretaker looks after 6 children. The ages (in years) of the children are given below: 

Here is the table from the image transcribed for you:

Child	Age (in years)
Meena	5
Aarav	4
Nisha	6
Kabir	4
Pooja	5

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(i) What is the nature (type) of the population of the ages of children?
(ii) Construct the sampling distribution of the sample mean for all possible samples of size n = 2.
(iii) Comment on whether the sampling distribution is approximately normal.
(iv) Find the mean and standard error of the sampling distribution. **(20)**

**3.** Let be a random sample from a population with mean and variance . Consider the estimator

$

(i) Find the bias of the estimator .
(ii) Find the variance of .
(iii) Hence, calculate the Mean Square Error (MSE) of . **(20)**

**4.** A survey was conducted to study the preference for online learning among students from urban and rural areas. Out of 300 urban students, 210 preferred online learning, while out of 250 rural students, 150 preferred online learning. Construct a 95% confidence interval for the difference between the population proportions of students preferring online learning in urban and rural areas. **(10)**

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5. A researcher wants to compare the average test scores of students taught using Method A and Method B. A random sample of students was selected from each group, and their scores are given below: 

Here is the text from the image organized into a clear table format:

Student	Method A	Method B
1	68	72
2	74	75
3	71	78
4	69	70
5	73	76
6	70	74
7	72	77
8	75	79

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Assuming that the populations are normally distributed with equal variances. For testing whether there is a significant difference between the mean scores of the two teaching methods at the 5% level of significance

(i) State the null and alternative hypotheses.

(ii) Name the appropriate t-test and justify your choice.

(iii) Compute the test statistic and critical value.

(iv) State your conclusion.

6. Let X1, X2, ..., Xbe a random sample from the Exponential distribution with pdf f(x; 0) = 0e-ex, x > 0, 0 > 0

(i) Obtain the maximum likelihood estimator (MLE) of 0.

(ii) Hence, find the maximum likelihood estimate of for the observed sample: 2.1, 1.6, 3.4, 0.9, 2.5

8. Describe the following:

(i) t-distribution

(ii) General procedure of Testing of hypothesis

MST 016 (January 2025 - July 2025) - ENGLISH

TUTOR MARKED ASSIGNMENT

MST-016: Statistical Inference

Course Code: MST-016

Assignment Code: MST-016/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) is a random sample of size 5 taken from an Exponential distribution, then estimator T₁ is more efficient than T2.

(ii)  are two estimators of the parameter such that Var(T₁) = 1/n and Var(T₂₎ = n then T₁ is more efficient than T₂.

(iii) A 95% confidence interval is smaller than a 99% confidence interval.

(iv) If the probability density function of a random variable X follows F-distribution is

then degrees of freedom of the distribution will be (2,2).

(v) A patient suffering from fever reaches to a doctor and suppose the doctor formulates the hypotheses as

Ho: The patient is a chikungunya patient

H₁: The patient is not a chikungunya patient

If the doctor rejects Ho when the patient is actually a chikunguniya patient, then the doctor commits type II error.

(b) Describe the various forms of the sampling distribution single mean.

2 A baby-sister has 6 children under her supervision. The age of each child is as follows:

Child	Age (in years
Sonu	2
Lavnik	4
Chiya	3
Amam	3
Avishi	4
Ridhi	5
Sidhi	3

(i) What is the form of population of age of children?

(ii) Prepare the sampling distribution of the sample mean when the sample size is 2.

(iii) Is the shape of the sampling distribution normal?

(iv) Calculate the mean and standard error of the sampling distribution.

 3. The department of transportation has mandated that the average speed of cars on interstate highways be no more than 70 km per hour in order. To check whether the people

followed it or not, a researcher took a random sample of 186 cars and found that the average speed was 72 km per hour with a standard deviation 0.6 km per hour.

(i) State null and alternative hypotheses.

(ii) Name the test which is suitable in this situation and why?

(iii) Calculate the value of test statistic and critical value.

(iv)Draw the conclusion on the basis of the applied test.

4 An engineer conducted an experiment to compare two metals: iron and copper, as bonding agents for an alloy material. Components of the alloy were bonded using the metals as bonding agents, and the pressures required to break the bonds were measured. The data for the breaking pressures are given in the following table:

S. No	Breaking Pressure
	Iron	Copper
1	72.7	73
2	69.6	67.2
3	83.4	75.3
4	78.9	61.4
5	75	74
6	71.6	69.5
7	85.7	69.8
8	73.5	73.8
9	70.4	68
10	84.2	76.1

 If the breaking pressures for both iron and copper are normally distributed, are the variances of the distributions of the breaking pressure of iron and copper equal at 5 % level of significance?

 5. Complete the following table, one is done for you:

S. No.	Test For	Name of the Test	Test Statistic
1	Population mean when population variance is known and population is normal	Z-test
2	Population mean when population variance is unknown and population is normal
3	Difference of two population means when samples are paired, and population of differences follows normal distribution.
4	Difference of two population means when samples are independent, and population of differences follows normal distribution.
5	Population variance when the population is normal distributed
6	Population variance when the population is not normal distributed

 

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