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September 2024 term · Statistics for Data Science II · BSMA1004

Stats 2 End Term: 22 December 2024, Set QDF1 (September 2024 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 22 Dec 2024, in the September 2024 term, set QDF1: 15 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
15
Marks
40
Duration
180 min
Numerical
5
MCQ
7
MSQ
3
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION DIPLOMA AN EXAM QDF3 22 Dec 2024 · No negative marking.

Question 1

+3 marksNumerical answer
Show answer

Correct answer: 0.17 (accepted within ±0.03)

Question 1 on its own page

Question 2

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

Correct answer

  • C
Question 2 on its own page

Question 3

+3 marksOne or more correct options

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

Select all that apply.

  1. A

    The power of a test is the probability of rejecting the null hypothesis when it is false.

  2. B

    The probability of accepting the alternative hypothesis when it is true is called as level of significance.

  3. C

    Type I error is the probability of rejecting the null hypothesis when alternative hypothesis is false.

  4. D

    If the probability of making a Type II error is 0.05, the power of the test is 0.95.

Show answer

Correct answers

  • A

    The power of a test is the probability of rejecting the null hypothesis when it is false.

  • C

    Type I error is the probability of rejecting the null hypothesis when alternative hypothesis is false.

  • D

    If the probability of making a Type II error is 0.05, the power of the test is 0.95.

Question 3 on its own pageAlso asked in End Term 22 Dec 2024

Question 4

+3 marksOne or more correct options

Select all that apply.

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

Correct answers

  • B
  • C
Question 4 on its own page

Question 5

+3 marksOne or more correct options

Select all that apply.

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

Correct answers

  • B
  • D
Question 5 on its own page

Question 6

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Consider a random sample (1, 0, 1, 2, 2, 0, 1). Find the method of moments estimate of θ for the given sample. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.43 (accepted within ±0.03)

Question 6 on its own page

Question 7

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Consider a random sample (2, 0, 1, 1, 2, 2, 1, 1, 0, 0). Find the maximum likelihood estimate of θ for the given sample. Enter the answer correct to one decimal place.

Show answer

Correct answer: 0.3 (accepted within ±0.03)

Question 7 on its own page

Question 8

+3 marksOne correct option

A company is testing a new AI-based chatbot for customer service and wants to know if it is liked by its users. Let p be the true proportion of users who would find the chatbot helpful. The team selected 30 customers randomly and asked if they found the chatbot useful. Out of these, 12 responded ‘yes’.
Based on the above data, answer the given subquestions.

Find the posterior distribution of p for a Beta [3, 2] prior.

  1. A

    Beta(12, 18)

  2. B

    Beta(15, 20)

  3. C

    Beta(14, 19)

  4. D

    Beta(20, 15)

Show answer

Correct answer

  • B

    Beta(15, 20)

Question 8 on its own page

Question 9

+2 marksNumerical answer

A company is testing a new AI-based chatbot for customer service and wants to know if it is liked by its users. Let p be the true proportion of users who would find the chatbot helpful. The team selected 30 customers randomly and asked if they found the chatbot useful. Out of these, 12 responded ‘yes’.
Based on the above data, answer the given subquestions.

Find the posterior mean using the correct prior from the previous question. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.43 (accepted within ±0.03)

Question 9 on its own page

Question 10

+2 marksOne correct option

The average battery life of smartphones for a certain model is 15 hours, with a standard deviation of 3 hours. An analyst suspects that the true average battery life is greater
than 15 hours. To test this, he takes a random sample of 100 smartphones and finds that the sample mean battery life is 17 hours.
Based on the above data, answer the given subquestions.

State the null and alternative hypotheses.

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

Correct answer

  • A
Question 10 on its own page

Question 11

+3 marksOne correct option

The average battery life of smartphones for a certain model is 15 hours, with a standard deviation of 3 hours. An analyst suspects that the true average battery life is greater
than 15 hours. To test this, he takes a random sample of 100 smartphones and finds that the sample mean battery life is 17 hours.
Based on the above data, answer the given subquestions.

What conclusion will you make for the given test?

  1. A
  2. B
Show answer

Correct answer

  • A
Question 11 on its own page

Question 12

+2 marksOne correct option

Based on the above data, answer the given subquestions.

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

Correct answer

  • B
Question 12 on its own page

Question 13

+3 marksOne correct option

Based on the above data, answer the given subquestions.

Are X and Y independent?

  1. A

    Yes

  2. B

    No

Show answer

Correct answer

  • A

    Yes

Question 13 on its own page

Question 14

+3 marksOne correct option

Based on the above data, answer the given subquestions.

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

Correct answer

  • B
Question 14 on its own page

Question 15

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 1.78 (accepted within ±0.03)

Question 15 on its own page