NPTEL Data Science For Engineers Week 3 Assignment Answers 2024

1. 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

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2. 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⁻¹_z(0.025)=−1.9599

Accept H₀
Reject H₀

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3. 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 :-

4. 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 :-

5. 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 :-

6. 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 :-

7. 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

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8. 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 :-

9. 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?