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September 2022 term · Statistics for Data Science II · BSMA1004

Stats 2 End Term: 11 December 2022, Set ETF1 (September 2022 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 11 Dec 2022, in the September 2022 term, set ETF1: 17 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
17
Marks
40
Duration
180 min
Numerical
9
MSQ
1
MCQ
7
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION AN1 EXAM ETF1 11 Dec 2022 · No negative marking.

Question 1

+3 marksNumerical answer
Show answer

Correct answer: 0.33 (accepted within ±0.03)

Question 1 on its own page

Question 2

+3 marksNumerical answer
Show answer

Correct answer: 0.12 (accepted within ±0.02)

Question 2 on its own page

Question 3

+3 marksOne or more correct options

Which of the following statements are correct?

Select all that apply.

  1. A

    The probability of accepting the Null hypothesis when it is not true is called as level of significance.

  2. B

    If the significance level of a test T is 0.1, then the power of the test T will be 0.9.

  3. C

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

  4. D

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

Show answer

Correct answers

  • C

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

  • D

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

Question 3 on its own pageAlso asked in End Term 11 Dec 2022

Question 4

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

Correct answer

  • A
Question 4 on its own page

Question 5

+3 marksOne correct option

Consider the following situations and match them with suitable test statistics and hypothesis tests: Suppose we observe samples from a normal distribution, where the variance is known. We want to check whether the mean is greater than μ. What test statistic and test can be applied for this situation?

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

Correct answer

  • A
Question 5 on its own page

Question 6

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Find the value of c.Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.25

Question 6 on its own page

Question 7

+1 markNumerical answer

Based on the above data, answer the given subquestions.

What is the probability that the unit temperature change is equal to 0.5?

Show answer

Correct answer: 0

Question 7 on its own page

Question 8

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

What is the probability that the unit pressure change during the chemical process is more than 0.5, given that the unit temperature change is equal to 0.5? Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.935 (accepted within ±0.025)

Question 8 on its own page

Question 9

+1 markOne correct option

Based on the above data, answer the given subquestions.

  1. A

    Yes

  2. B

    No

Show answer

Correct answer

  • A

    Yes

Question 9 on its own page

Question 10

+2 marksOne correct option

Based on the above data, answer the given subquestions.

Assume θ is an unknown parameter. Find the maximum likelihood estimate of θ.

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

Correct answer

  • A
Question 10 on its own page

Question 11

+2 marksOne correct option

Based on the above data, answer the given subquestions.

Consider θ as a random variable with prior distribution as Uniform [0,1]. Choose the correct options from the following:

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

Correct answer

  • C
Question 11 on its own page

Question 12

+3 marksOne correct option

We wish to estimate the probability p of getting the number four on a biased die using a Bayesian estimator. Consider 10 independent throws and let X be the number of times four appears on the die. Assume the prior distribution of p to be Beta(1, 1).
Based on the above data, answer the given subquestions.

Out of 10 throws, if four appeared a total of five times, find the posterior distribution of p .

  1. A

    Bernoulli(0.4)

  2. B

    Beta(4, 4)

  3. C

    Beta(6, 6)

  4. D

    Bernoulli(0.6)

Show answer

Correct answer

  • C

    Beta(6, 6)

Question 12 on its own page

Question 13

+2 marksNumerical answer

We wish to estimate the probability p of getting the number four on a biased die using a Bayesian estimator. Consider 10 independent throws and let X be the number of times four appears on the die. Assume the prior distribution of p to be Beta(1, 1).
Based on the above data, answer the given subquestions.

Find the posterior mean using the given prior. Enter the answer correct to one decimal place.

Show answer

Correct answer: 0.5 (accepted within ±0.1)

Question 13 on its own page

Question 14

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the method of moments estimate of θ for the given sample. Enter the answer correct to one decimal place.

Show answer

Correct answer: 1.2 (accepted within ±0.1)

Question 14 on its own page

Question 15

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the maximum likelihood estimate of θ for the given sample. Enter the answer correct to one decimal place.

Show answer

Correct answer: 1.4 (accepted within ±0.1)

Question 15 on its own page

Question 16

+2 marksOne correct option

An urn contains some blue balls and some red balls. Shalini claims that if a ball is picked randomly from the urn, then the probability p that the ball will be blue is 0.2. Suspecting that 0.2 is too high, Nandan decided to pick 10 balls randomly. If two or more blue balls are picked out of those 10 balls, then he accepts Shalini’s claim or else he rejects it.
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 16 on its own page

Question 17

+3 marksNumerical answer

An urn contains some blue balls and some red balls. Shalini claims that if a ball is picked randomly from the urn, then the probability p that the ball will be blue is 0.2. Suspecting that 0.2 is too high, Nandan decided to pick 10 balls randomly. If two or more blue balls are picked out of those 10 balls, then he accepts Shalini’s claim or else he rejects it.
Based on the above data, answer the given subquestions.

Find the significance level of the test. Enter the answer correct to three decimal places.

Show answer

Correct answer: 0.375 (accepted within ±0.015)

Question 17 on its own pageAlso asked in End Term 11 Dec 2022