Stats 2 End Term: 11 December 2022, Set ETF1-2 (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 ETF1-2: 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.
- 17
- 40
- 180 min
- 9
- 1
- 7
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Correct answer: 0.33 (accepted within ±0.03)
Question 2
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Correct answer: 0.24 (accepted within ±0.02)
Question 3
Which of the following statements are correct?
The probability of accepting the Null hypothesis when it is not true is called as level of significance.
If the significance level of a test T is 0.1, then the power of the test T will be 0.9.
Type II error is the probability of accepting the Null hypothesis when it is not true.
The probability of rejecting the Null hypothesis when it is true is called as level of significance.
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Correct answers
Type II error is the probability of accepting the Null hypothesis when it is not true.
The probability of rejecting the Null hypothesis when it is true is called as level of significance.
Question 4
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Correct answer
Question 5
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 unknown. We want to check whether the mean is greater than μ. What test statistic and test can be applied for this situation?
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Correct answer
Question 6
Based on the above data, answer the given subquestions.
Find the value of c.
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Correct answer: 1
Question 7
Based on the above data, answer the given subquestions.
What is the probability that the unit temperature change is equal to 0.5?
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Correct answer: 0
Question 8
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.
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Correct answer: 0.935 (accepted within ±0.025)
Question 9
Based on the above data, answer the given subquestions.
Yes
No
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Correct answer
Yes
Question 10
Based on the above data, answer the given subquestions.
Assume θ is an unknown parameter. Find the maximum likelihood estimate of θ.
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Correct answer
Question 11
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:
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Correct answer
Question 12
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 three times, find the posterior distribution of p .
Bernoulli(0.3)
Beta(4, 8)
Beta(3, 7)
Bernoulli(0.5)
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Correct answer
Beta(4, 8)
Question 13
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 two decimal places.
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Correct answer: 0.33 (accepted within ±0.01)
Question 14
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.
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Correct answer: 1.8 (accepted within ±0.1)
Question 15
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.
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Correct answer: 1.6 (accepted within ±0.1)
Question 16
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.
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Correct answer
Question 17
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.
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Correct answer: 0.375 (accepted within ±0.015)