Nptel Data Science for Engineers Assignment 3 Answers

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Nptel Data Science for Engineers Assignment 3 Answers
Nptel Data Science for Engineers Assignment 3 Answers

Nptel Data Science for Engineers Assignment 3 Answers (July-Dec 2024)


Q1. Sumit wants to contact one of his friends, but he remembers only the first 9 of the 10 digits of the contact number. He is sure that the last digit of the contact number is an odd number. He selects an odd number randomly. If the random variable X
denotes the last digit of the contact number, then calculate Var(X).
5
8
33
None of the above

Answer:


Q2Suppose X∼Normal (μ, 4). For n = 20 iid samples of X, the observed sample mean is 5.2. What conclusion would a z -test reach if the null hypothesis assumes μ = 5 (against an alternative hypothesis μ≠5) at a significance level of α=0.05?
Use F−1z(0.025)=−1.9599

Accept H0

Reject H0

Answer:


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These are Nptel Data Science for Engineers Assignment 3 Answers


Q3.A box contains 8 items out of which 2 are defective. A sample of 5 items is to be selected randomly (without replacement) from the box. If the random variable X
represents the number of defective items in a selection of 5 items, then find E(X)
.(Enter the answer correct to 2 decimal places)
1.25
5
0.4
1.3

Answer:


Q4.Suppose X∼ Normal(μ , 9). For n=100 iid samples of X , the observed sample mean is 11.8. What conclusion would a z-test reach if the null hypothesis assumes μ=10.5 (against an alternative hypothesis μ≠10.5)?

Accept H0
at a significance level of 0.10
.

Reject H0
at a significance level of 0.10
.

Accept H0
at a significance level of 0.05
.

Reject H0
at a significance level of 0.05

Answer:


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These are Nptel Data Science for Engineers Assignment 3 Answers


Q5. Let X and Y be two independent random variables with Var(X) = 9 and Var(Y) = 3, find Var(4X− 2Y6).
100
140
156
None of the above

Answer:


Q6.The correlation coefficient of two random variable X and Y is 14, their variance is given by 3 and 5. Compute Cov(X,Y).
-0.854
0.561
-0.968
None of the above

Answer:


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These are Nptel Data Science for Engineers Assignment 3 Answers


Q7.When will you reject the Null hypothesis?

p value greater than α

p value less than α

p value equal to α
None of the above

Answer:


Q8. A sample of N observations are independently drawn from a normal distribution. The sample variance follows
Normal distribution

Chi-square with N degrees of freedom

Chi-square with N − 1 degrees of freedom

t-distribution with N− 1 degrees of freedom

Answer:


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These are Nptel Data Science for Engineers Assignment 3 Answers


Q9. A car manufacturer purchases car batteries from two different suppliers. Supplier X
provides 55% of the batteries and supplier Y provides the rest. 5% of all batteries from supplier X
are defective and 4% of all batteries from supplier Y are defective. You select a battery from the bulk and you found it to be defective. What is the probability that it is from Supplier X?
0.0455
0.455
0.604
0.018

Answer:


Q10. Which one of the following is best measure of central tendency for categorical data?
Mean
Median
Mode
None of the above

See also  Data Science for Engineers | Week 1

Answer:


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Nptel Data Science for Engineers Assignment 3 Answers (Jan-Apr 2024)

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These are NPTEL Data Science for Engineers Assignment 3 Answers


Q1. Sumit wants to contact one of his friends, but he remembers only the first 9 of the 10 digits of the contact number. He is sure that the last digit of the contact number is an odd number. He selects an odd number randomly. If the random variable X denotes the last digit of the contact number, then calculate Var(X).
5
8
33
None of the above

Answer: 8


Q2. Suppose X∼Normal (μ,4). For n=20 iid samples of X, the observed sample mean is 5.2. What conclusion would a z-test reach if the null hypothesis assumes μ=5(against an alternative hypothesis μ≠5) at a significance level of α=0.05? Use F−1z(0.025)=−1.9599
Accept H0
Reject H0

Answer: Accept H0


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These are NPTEL Data Science for Engineers Assignment 3 Answers


Q3. A box contains 8 items out of which 2 are defective. A sample of 5 items is to be selected randomly (without replacement) from the box. If the random variable X represents the number of defective items in a selection of 5 items, then find E(X).(Enter the answer correct to 2 decimal places)
1.25
5
0.25
1

Answer:


Q4. Suppose X∼Normal(μ,9). For n=100 iid samples of X, the observed sample mean s 11.8. What conclusion would a z-test reach if the null hypothesis assumes μ=10.5(against an alternative hypothesis μ≠10.5)?

Accept H0 at a significance level of 0.10.
Reject H0 at a significance level of 0.10.
Accept H0 at a significance level of 0.05.
Reject H0 at a significance level of 0.05.

Answer: a, d


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These are NPTEL Data Science for Engineers Assignment 3 Answers


Q5. Let X and Y be two independent random variables with Var(X)=9 and Var(Y)=3, find Var(4X−2Y+6).
100
140
156
None of the above

Answer: 156


Q6. The correlation coefficient of two random variable X and Y is 14, their variance is given by 3 and 5. Compute Cov(X,Y).
-0.854
0.561
-0.968
None of the above

Answer: -0.968


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These are NPTEL Data Science for Engineers Assignment 3 Answers


Q7. When will you reject the Null hypothesis?
p value greater than α
p value less than α
p value equal to α
None of the above

Answer: p value less than α


Q8. A sample of N observations are independently drawn from a normal distribution. The sample variance follows
Normal distribution
Chi-square with N degrees of freedom
Chi-square with N−1 degrees of freedom
t-distribution with N−1 degrees of freedom

Answer: Chi-square with N−1 degrees of freedom


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These are NPTEL Data Science for Engineers Assignment 3 Answers


Q9. A car manufacturer purchases car batteries from two different suppliers. Supplier X provides 55% of the batteries and supplier Y rovides the rest. 5% of all batteries from supplier X are defective and 4% of all batteries from supplier Y are defective. You select a battery from the bulk and you found it to be defective. What is the probability that it is from Supplier X?
0.0455
0.455
0.0275
0.018

Answer: 0.0275


Q10. Which one of the following is best measure of central tendency for categorical data?
Mean
Median
Mode
None of the above

See also  Data Science for Engineers | Week 2

Answer: Mode


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Nptel Data Science for Engineers Assignment 3 Answers (July-Dec 2023)

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These are Nptel Data Science for Engineers Week 3 Assignment Answers


A six sided die is marked ‘1’ on one face, ‘2’ on two of its faces, and ‘3’ on the remaining three faces. The die is thrown twice. Let X denotes the total score in two throws.
Based on the above information, answer questions (1), (2).

Q1. Find the value of P(X>2.5|X<5). (Enter the answer correct to 2 decimal places).

Answer: (Type: Range) 0.80,0.94


Q2. Find the expected value of X.

Answer: (Type: Range) 4,4.7


These are Nptel Data Science for Engineers Week 3 Assignment Answers


Q3. Suppose X∼ Normal(μ,4). For n=20 iid samples of X, the observed sample mean is 5.2. What conclusion would a z-test reach if the null hypothesis assumes μ=5(against an alternative hypothesis μ≠5) at a significance level of α=0.05? Use F−1z(0.025)=−1.9599
Accept H0
Reject H0

Answer: Accept H0


Q4. A pharmaceutical company is testing a new drug. The probability that a patient experiencing a side effect from this drug is 0.10. If the drug is given to 5 patients, what is the probability that more than 1 patient will experience the side effect? (Enter the answer correct to 2decimal places.)

Answer: (Type: Range) 0.05,0.11


These are Nptel Data Science for Engineers Week 3 Assignment Answers


Q5. Suppose X∼Normal(μ,9). For n=100 iid samples of X, the observed sample mean is 11.8. What conclusion would a z-test reach if the null hypothesis assumes μ=10.5(against an alternative hypothesis μ≠10.5)?
Accept H0 at a significance level of 0.10.
Reject H0 at a significance level of 0.10.
Accept H0 at a significance level of 0.05.
Reject H0 at a significance level of 0.05.

Answer: b, c


Q6. Let X and Y be two independent random variables with Var(X)=9 and Var(Y)=3, find Var(4X−2Y+6).
100
140
156
None of the above

Answer: 156


These are Nptel Data Science for Engineers Week 3 Assignment Answers


Q7. The correlation coefficient of two random variable X and Y is −14, their variance is given by 3 and 5. Compute Cov(X,Y).
-0.854
0.561
-0.968
None of the above

Answer: None of the above


Q8. A sample of N observations are independently drawn from a normal distribution. The sample variance follows
Normal distribution
Chi-square with N degrees of freedom
Chi-square with N−1 degrees of freedom
t -distribution with N−1 degrees of freedom

Answer: Chi-square with N−1 degrees of freedom


These are Nptel Data Science for Engineers Week 3 Assignment Answers


Q9. A car manufacturer purchases car batteries from two different suppliers. Supplier X provides 55% of the batteries and supplier Y provides the rest. 5% of all batteries from supplier X are defective and 4% of all batteries from supplier Y are defective. You select a battery from the bulk and you found it to be defective. What is the probability that it is from Supplier X?
0.0455
0.455
0.0275
0.018

Answer: 0.0275


Q10. Find the t -statistic for the sample data, given that the population mean of the distribution is 8.
-3.155
8.33
-2.99
None of the above

Answer: None of the above


These are Nptel Data Science for Engineers Week 3 Assignment Answers


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Nptel Data Science for Engineers Assignment 3 Answers (Jan-Apr 2023)

Course Name: Data Science for Engineers

Course Link: Click Here

These are NPTEL Data Science for Engineers Assignment 3 Answers


Q1. Sumit wants to contact one of his friends, but he remembers only the first 9 of the 10 digits of the contact number. He is sure that the last digit of the contact number is an odd number. He selects an odd number randomly. If the random variable X denotes the last digit of the contact number, then calculate Var(X).
a. 5
b. 8
c. 33
d. None of the above

See also  Data Science for Engineers | Week 7

Answer: b. 8


Q2. Suppose X∼Normal(µ,4). For n=20 iid samples of X, the observed sample mean is 5.2. What conclusion would a z-test reach if the null hypothesis assumes µ=5 (against an alternative hypothesis µ≠5) at a significance level of α=0.05?
Use F−1z(0.025)=−1.9599

a. Accept H0
b. Reject H0

Answer: a. Accept H0


These are Nptel Data Science for Engineers Week 3 Assignment Answers


Q3. A box contains 8 items out of which 2 are defective. A sample of 5 items is to be selected randomly (without replacement) from the box. If the random variable X represents the number of defective items in a selection of 5 items, then find E(X).(Enter the answer correct to 2 decimal places)
a. 1.25
b. 5

Answer: a. 1.25


Q4. Suppose X∼Normal(μ,9). For n=100 iid samples of X, the observed sample mean is 11.8. What conclusion would a z-test reach if the null hypothesis assumes μ=10.5(against an alternative hypothesis μ≠10.5)?
a. Accept H0 at a significance level of 0.10.
b. Reject H0 at a significance level of 0.10.
c. Accept H0 at a significance level of 0.05.
d. Reject H0 at a significance level of 0.05.

Answer: d. Reject H0 at a significance level of 0.05.


These are Nptel Data Science for Engineers Week 3 Assignment Answers


Q5. Let X and Y be two independent random variables with Var(X)=9 and Var(Y)=3, find Var(4X−2Y+6).
a. 100
b. 140
c. 156
d. None of the above

Answer: c. 156


Q6. The correlation coefficient of two random variable X and Y is 14, their variance is given by 3 and 5. Compute Cov(X,Y).
a. -0.854
b. 0.561
c. -0.968
d. None of the above

Answer: d. None of the above


These are Nptel Data Science for Engineers Week 3 Assignment Answers


Q7. When will you reject the Null hypothesis?
a. p value greater than α
b. p value less than α
c. p value equal to α
d. None of the above

Answer: b. p value less than α


Q8. A sample of N observations are independently drawn from a normal distribution. The sample variance follows
a. Normal distribution
b. Chi-square with N degrees of freedom
c. Chi-square with N−1 degrees of freedom
d. t-distribution with N−1 degrees of freedom

Answer: c. Chi-square with N−1 degrees of freedom


These are Nptel Data Science for Engineers Week 3 Assignment Answers


Q9. A car manufacturer purchases car batteries from two different suppliers. Supplier X provides 55% of the batteries and supplier Y provides the rest. 5% of all batteries from supplier X are defective and 4% of all batteries from supplier Y are defective. You select a battery from the bulk and you found it to be defective. What is the probability that it is from Supplier X?
a. 0.0455
b. 0.455
c. 0.0275
d. 0.018

Answer: b. 0.455


These are Nptel Data Science for Engineers Week 3 Assignment Answers


Q10. Which one of the following is best measure of central tendency for categorical data?
a. Mean
b. Median
c. Mode
d. None of the above

Answer: c. Mode


These are Nptel Data Science for Engineers Week 3 Assignment Answers

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