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Stats II · All 2024 papers

30 questions · 80 marks · 2 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Statistics for Data Science II

All 2024 papers

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

End Term · 22 Dec 2024 (FN)End Term

Q1NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q2MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q3MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following statement(s) is(are) correct?
1. AThe power of a test is the probability of rejecting the null hypothesis when it is false.
2. BThe probability of accepting the alternative hypothesis when it is true is called as level of significance.
3. CType I error is the probability of rejecting the null hypothesis when alternative hypothesis is false.
4. DIf the probability of making a Type II error is 0.05, the power of the test is 0.95.
Q4MSQ3 Marks·Choose all correct options
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q5MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q6–Q7
Based on the above data, answer the given subquestions.
Q6NAT2 Marks·Write the number
Asked 5 times Key ↓
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.
Your answer:
Q7NAT3 Marks·Write the number
Asked 4 times Key ↓
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.
Your answer:
Read the passage below, then answer Q8–Q9
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.
Q8MCQ3 Marks·Choose one option
Asked 4 times Key ↓
Find the posterior distribution of p for a Beta [3, 2] prior.
1. ABeta(12, 18)
2. BBeta(15, 20)
3. CBeta(14, 19)
4. DBeta(20, 15)
Q9NAT2 Marks·Write the number
Asked 2 times Key ↓
Find the posterior mean using the correct prior from the previous question. Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q10–Q11
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.
Q10MCQ2 Marks·Choose one option
Asked 4 times Key ↓
State the null and alternative hypotheses.
1. A
2. B
3. C
4. D
Q11MCQ3 Marks·Choose one option
Asked 2 times Key ↓
What conclusion will you make for the given test?
1. A
2. B
Read the passage below, then answer Q12–Q13
Based on the above data, answer the given subquestions.
Q12MCQ2 Marks·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q13MCQ3 Marks·Choose one option
Key ↓
Are X and Y independent?
1. AYes
2. BNo
Read the passage below, then answer Q14–Q15
Based on the above data, answer the given subquestions.
Q14MCQ3 Marks·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q15NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:

End Term · 22 Dec 2024 (AN)End Term

Q16NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q17MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q18MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q19MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following statement(s) is(are) correct?
1. AThe power of a test is the probability of rejecting the null hypothesis when it is false.
2. BThe probability of accepting the alternative hypothesis when it is true is called as level of significance.
3. CType I error is the probability of rejecting the null hypothesis when alternative hypothesis is false.
4. DIf the probability of making a Type II error is 0.05, the power of the test is 0.95.
Q20MSQ3 Marks·Choose all correct options
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q21–Q22
Based on the above data, answer the given subquestions.
Q21NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q22NAT2 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q23–Q24
Let p be the true proportion of customers who favor a newly introduced feature in our mobile app. The product team randomly selected 50 customers and asked them if they appreciate the new feature. From the survey, 20 out of the 50 customers responded with a ‘yes’.
Based on the above data, answer the given subquestions.
Q23MCQ3 Marks·Choose one option
Asked 4 times Key ↓
Find the posterior distribution of p for a Uniform [0, 1] prior.
1. ABeta(20, 30)
2. BBeta(30, 20)
3. CBeta(21, 31)
4. DBeta(31, 21)
Q24NAT2 Marks·Write the number
Asked 2 times Key ↓
Find the posterior mean. Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q25–Q26
A packaging company uses a machine to fill packets with 98.5 gram of powdered material. A quality control manager suspects that the machine is underfilling the packets. To investigate, he collects a random sample of 100 packets and measures the weights. The sample reveals an average weight of 98.29 gram, with a standard deviation of 1.2 gram.
Based on the above data, answer the given subquestions.
Q25MCQ2 Marks·Choose one option
Asked 4 times Key ↓
State the null and alternative hypotheses.
1. A
2. B
3. C
4. D
Q26MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Choose the set of correct options.
1. A
2. B
3. C
4. D
Read the passage below, then answer Q27–Q28
Based on the above data, answer the given subquestions.
Q27MCQ2 Marks·Choose one option
Asked 5 times Key ↓
Find the Marginal distribution of X.
1. A
2. B
3. C
4. D
Q28NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q29–Q30
Based on the above data, answer the given subquestions.
Q29MCQ3 Marks·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q30NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q10.14 to 0.2

Q2C

Q3A, C, D

Q4B, C

Q5B, D

Q60.4 to 0.46

Q70.27 to 0.33

Q8B

Q90.4 to 0.46

Q10A

Q11A

Q12B

Q13A

Q14B

Q151.75 to 1.81

Q160.16 to 0.22

Q17A

Q18A

Q19A, C, D

Q20A, D

Q210.57 to 0.63

Q220.69 to 0.75

Q23C

Q240.37 to 0.43

Q25C

Q26A, B

Q27B

Q280.3 to 0.36

Q29C

Q301.3 to 1.36

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