Stats 2 End Term: 22 August 2021 (May 2021 term)
The IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 22 Aug 2021, in the May 2021 term: 20 questions for 50 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.
- 20
- 50
- 180 min
- 10
- 10
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Correct answer: 0.19 (accepted within ±0.02)
Question 2
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Correct answer: 0.275 (accepted within ±0.015)
Question 3
Shruti will read either one chapter of her Geography book or one chapter of her history book with equal probability. The number of misprints in a chapter of her Geography book is Poisson distributed with mean 4 and the number of misprints in a chapter of her history book is Poisson distributed with mean 7. What is the expected number of misprints that she will come across in a chapter? Enter your answer correct to one decimal place.
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Correct answer: 5.5 (accepted within ±0.1)
Question 4
Based on the above data, answer the given subquestions.
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Correct answer
Question 5
Based on the above data, answer the given subquestions.
Find the method of moments estimate of θ from the samples 8, 3, 1, 7, 8, 4, 10, 9, 2, 6. Enter your answer correct to two decimal places.
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Correct answer: 4.35 (accepted within ±0.02)
Question 6
Based on the above data, answer the given subquestions.
Determine the value of the test statistic when testing the independence of gender and voting. Enter your answer correct to two decimal places.
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Correct answer: 2.855 (accepted within ±0.085)
Question 7
Based on the above data, answer the given subquestions.
Yes
No
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Correct answer
Yes
Question 8
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Correct answer
Question 9
A null hypothesis will be rejected when the value of the test statistic is large. The observed value of the test statistic is 3.6. Suppose that when the null hypothesis is true, the probability that the test statistic is at least 3.6 is 0.04.
Based on the above data, answer the given subquestions.
Will the null hypothesis be rejected at a significance level of 1%?
Yes
No
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Correct answer
No
Question 10
A null hypothesis will be rejected when the value of the test statistic is large. The observed value of the test statistic is 3.6. Suppose that when the null hypothesis is true, the probability that the test statistic is at least 3.6 is 0.04.
Based on the above data, answer the given subquestions.
Will the null hypothesis be rejected at a significance level of 5%?
Yes
No
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Correct answer
Yes
Question 11
An experiment was conducted to compare the alcohol content of cough syrup on two different production lines. It is suspected that variability of alcohol content is more on the production line 1. A sample of ten cough syrups from production line 1 has a sample standard deviation (s1) of 3.8, while a sample of twelve cough syrups from production line 2 has a sample standard deviation (s2) of 3.4.
Based on the above data, answer the given subquestions.
State the null and alternative hypothesis.
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Correct answer
Question 12
An experiment was conducted to compare the alcohol content of cough syrup on two different production lines. It is suspected that variability of alcohol content is more on the production line 1. A sample of ten cough syrups from production line 1 has a sample standard deviation (s1) of 3.8, while a sample of twelve cough syrups from production line 2 has a sample standard deviation (s2) of 3.4.
Based on the above data, answer the given subquestions.
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Correct answer: 0.35 (accepted within ±0.03)
Question 13
From previous data, we know that the annual rainfall, X in a particular region is normally distributed with E(X) = 650 mm. In recent years, due to various climate changes, it is hypothesized that in fact, the annual rainfall has increased. Let us assume that the rainfall (in mm) registered in the past 8 years are as follows:
650, 802, 400, 550, 690, 700, 750, 690.
Based on the above data, answer the given subquestions.
Identify the null and alternative hypotheses:
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Correct answer
Question 14
From previous data, we know that the annual rainfall, X in a particular region is normally distributed with E(X) = 650 mm. In recent years, due to various climate changes, it is hypothesized that in fact, the annual rainfall has increased. Let us assume that the rainfall (in mm) registered in the past 8 years are as follows:
650, 802, 400, 550, 690, 700, 750, 690.
Based on the above data, answer the given subquestions.
Fail to reject the null hypothesis.
Reject the null hypothesis.
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Correct answer
Fail to reject the null hypothesis.
Question 15
An editor of a newspaper wants to conduct a survey in order to estimate the proportion (p) of voters in the city. She uses a Beta(a, b) prior distribution for p. Data from other similar cities suggests an expected value of 0.5 and standard deviation of 0.15 for the proportion of voters. Based on the above data, answer the given subquestions.
Find the value of a and b.
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Correct answer
Question 16
An editor of a newspaper wants to conduct a survey in order to estimate the proportion (p) of voters in the city. She uses a Beta(a, b) prior distribution for p. Data from other similar cities suggests an expected value of 0.5 and standard deviation of 0.15 for the proportion of voters. Based on the above data, answer the given subquestions.
Find the posterior mean if out of a sample of 100 people she surveyed, 40 are voters. Enter the answer correct to two decimal places.
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Correct answer: 0.41 (accepted within ±0.02)
Question 17
Based on the above data, answer the given subquestions.
What is the ML estimate of p. Write your answer correct to two decimal places.
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Correct answer: 0.70
Question 18
Based on the above data, answer the given subquestions.
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Correct answer: 4 (accepted within ±0.1)
Question 19
Based on the above data, answer the given subquestions.
No
Yes
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Correct answer
Yes
Question 20
NOTE: Enter your answer to the nearest integer.
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Correct answer: 7