Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
Statistics for Data Science II
End Term · 22 Dec 2024 (Forenoon)
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.
- Q1NAT3 Marks·Write the number
Your answer: - Q2MCQ3 Marks·Choose one option
- A
- B
- C
- D
- A
- Q3MSQ3 Marks·Choose all correct options
Which of the following statement(s) is(are) correct?
- AThe power of a test is the probability of rejecting the null hypothesis when it is false.
- BThe probability of accepting the alternative hypothesis when it is true is called as level of significance.
- CType I error is the probability of rejecting the null hypothesis when alternative hypothesis is false.
- 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
- A
- B
- C
- D
- A
- Q5MSQ3 Marks·Choose all correct options
- A
- B
- C
- D
- A
Read the passage below, then answer Q6–Q7
Based on the above data, answer the given subquestions.
Q6NAT2 Marks·Write the numberConsider 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
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 optionFind the posterior distribution of p for a Beta [3, 2] prior.
- ABeta(12, 18)
- BBeta(15, 20)
- CBeta(14, 19)
- DBeta(20, 15)
- Q9NAT2 Marks·Write the number
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 optionState the null and alternative hypotheses.
- A
- B
- C
- D
- A
- Q11MCQ3 Marks·Choose one option
What conclusion will you make for the given test?
- A
- B
- A
Read the passage below, then answer Q12–Q13
Based on the above data, answer the given subquestions.
Q12MCQ2 Marks·Choose one option
- A
- B
- C
- D
- A
- Q13MCQ3 Marks·Choose one option
Are X and Y independent?
- AYes
- BNo
Read the passage below, then answer Q14–Q15
Based on the above data, answer the given subquestions.
Q14MCQ3 Marks·Choose one option
- A
- B
- C
- D
- A
- Q15NAT2 Marks·Write the number
Your answer: