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May 2023 term · Statistics for Data Science II · BSMA1004

Stats 2 End Term: 3 September 2023, Set QPE1-S1 (May 2023 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 3 Sept 2023, in the May 2023 term, set QPE1-S1: 16 questions for 40 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
16
Marks
40
Duration
180 min
Numerical
8
MCQ
5
MSQ
3
Take as mock testPractise with answers

Updated

Official paper: IIT M DEGREE ET1 EXAM QPE1 S2 03 Sep · No negative marking.

Question 1

+3 marksNumerical answer
Show answer

Correct answer: 0.25 (accepted within ±0.02)

Question 1 on its own page

Question 2

+3 marksNumerical answer
Show answer

Correct answer: 0.67 (accepted within ±0.03)

Question 2 on its own page

Question 3

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • C
Question 3 on its own page

Question 4

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • D
Question 4 on its own page

Question 5

+3 marksOne or more correct options

Which of the following statement(s) is (are) correct?

Select all that apply.

  1. A

    Type II error is the probability of accepting the Null hypothesis when it is not true.

  2. B

    The probability of accepting the null hypothesis when it is false is equal to the power of the test.

  3. C

    The probability of rejecting the Null hypothesis when it is true is called the level of significance.

  4. D

    If the P-value of a test is 0.04, then the corresponding test will reject the null hypothesis at the significance level of 0.03.

Show answer

Correct answers

  • A

    Type II error is the probability of accepting the Null hypothesis when it is not true.

  • C

    The probability of rejecting the Null hypothesis when it is true is called the level of significance.

Question 5 on its own pageAlso asked in End Term 3 Sept 2023

Question 6

+2 marksOne or more correct options

An employee at a railway ticket counter serves customers in the queue individually. Suppose that the service time Xi for the i^(th) customer has mean E[Xi] = 2 and Var(Xi) = 1. Assume that service times for different customers are independent. Let Y be the total time the employee spends to serve 100 customers.
Based on the above data, answer the given subquestions.

Which of the following option(s) is(are) true?

Select all that apply.

  1. A

    E[Y] = 100

  2. B

    E[Y] = 200

  3. C

    Var(Y)= 100

  4. D

    Var(Y) = 50

Show answer

Correct answers

  • B

    E[Y] = 200

  • C

    Var(Y)= 100

Question 6 on its own page

Question 7

+3 marksNumerical answer

An employee at a railway ticket counter serves customers in the queue individually. Suppose that the service time Xi for the i^(th) customer has mean E[Xi] = 2 and Var(Xi) = 1. Assume that service times for different customers are independent. Let Y be the total time the employee spends to serve 100 customers.
Based on the above data, answer the given subquestions.

Using the Central Limit Theorem, find an approximate value for P(190 < Y < 210). Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.68 (accepted within ±0.02)

Question 7 on its own page

Question 8

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Find the value of k.
Enter the answer correct to one decimal place.

Show answer

Correct answer: 1.5

Question 8 on its own page

Question 9

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.625

Question 9 on its own page

Question 10

+2 marksOne correct option

Based on the above data, answer the given subquestions.

Find the expected value of X.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 10 on its own page

Question 11

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the method of moments estimate of p. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.37 (accepted within ±0.03)

Question 11 on its own page

Question 12

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the maximum likelihood estimate of p. Enter the answer correct to one decimal place.

Show answer

Correct answer: 0.4

Question 12 on its own page

Question 13

+3 marksOne correct option

The number of tosses required to get the first head on tossing a coin follows the Geometric(θ) distribution. The number of tosses observed to get the first head in 5 different i.i.d. repetitions are 2, 4, 5, 1, 3. Assume prior distribution of θ to be Beta(3, 4).
Based on the above data, answer the given subquestions.

Find the posterior distribution of θ.

  1. A

    Gamma(8, 14)

  2. B

    Beta(7, 13)

  3. C

    Beta(8, 14)

  4. D

    Beta(8, 19)

Show answer

Correct answer

  • C

    Beta(8, 14)

Question 13 on its own page

Question 14

+2 marksNumerical answer

The number of tosses required to get the first head on tossing a coin follows the Geometric(θ) distribution. The number of tosses observed to get the first head in 5 different i.i.d. repetitions are 2, 4, 5, 1, 3. Assume prior distribution of θ to be Beta(3, 4).
Based on the above data, answer the given subquestions.

Find the posterior mean. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.36 (accepted within ±0.03)

Question 14 on its own page

Question 15

+2 marksOne correct option

A factory has a machine that dispenses 98.5 ml of liquid in a bottle. An employee believes that the average amount of liquid in a bottle is less than 98.5 ml. He took a sample of 100 random bottles from the factory and found out that the average amount of liquid in a bottle is 98.29 ml with a standard deviation of 1.2 ml.
Based on the above data, answer the given subquestions.

Define null hypothesis and alternative hypothesis.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • C
Question 15 on its own page

Question 16

+3 marksOne or more correct options

A factory has a machine that dispenses 98.5 ml of liquid in a bottle. An employee believes that the average amount of liquid in a bottle is less than 98.5 ml. He took a sample of 100 random bottles from the factory and found out that the average amount of liquid in a bottle is 98.29 ml with a standard deviation of 1.2 ml.
Based on the above data, answer the given subquestions.

Choose the set of correct options.

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • B
Question 16 on its own page