NPTEL week 7
Week 7: Assignment 7
(Submitted on 2025-03-06, 00:03 IST)
1. pH of a solution is defined as a random variable (X). It is
Continuous
f(X=7) = 0
f(X=7) = 0.5
Discrete
2. A continuous random variable is said to have a uniform probability distribution f in the interval [A, B] if
f = B−A
f = 1/(B−A)
f = 1
f = 1/(B−A)²
3. In a normal distribution, the parameters are μ = 5 and σ = 2. This means that
The ratio of mean to standard deviation of the distribution is 2.5
The variance of the distribution is 4
The area under the normal probability distribution from x=2 to x=5 is the same as the area from x=5 to x=8
ALL of the above
4. For the data given below, the trimmed mean is calculated by discarding 10% of the lowest data and 10% of the largest data. The trimmed mean value is
27.793
27.838
27.960
28.041
5. The sample variance s² with n entities is
An unbiased estimator of the population variance σ²
A biased estimator of the population variance
Based on n-1 independent deviations from the mean
Generally equal to the population variance σ²
6. If there are 5 independent standard normal variables i.e. Z₁², Z₂², …, Z₅², then the sum of these will correspond to a
Standard normal distribution with mean value of 5
F-distribution with 5 degrees of freedom in both numerator and denominator
Chi-square distribution with 4 degrees of freedom
Chi-square distribution with 5 degrees of freedom
7. In industries, unless there is heavy competition, the managers would like to keep the existing process/operation going, as the profits are coming. If a new process/operation is suggested by a fresh recruit, the manager’s null hypothesis will be
Implement the new idea as it is going to be better than the existing one
Existing process is good and process modification will not bring about a substantial improvement, so maintain status quo
Reject the new idea outright without even testing it
Fire the fresh recruit
8. A river is suspected of pollution by a nearby chemical plant. Studies on the water samples revealed that the mean concentration is 10 ppm more than the stipulated limit. The plant will be found guilty if
If the null hypothesis is rejected
If the null hypothesis is accepted
If the p-value from the hypothesis testing using a suitable probability distribution and parameters is very low (<0.001)
If the occurrence of 10 ppm in excess is highly improbable to be attributed to acceptable variation from the true mean value
9. The weldability of a metal beam depends on the composition of manganese in it. Five different compositions are tested to find the effect on the weldability. For each composition, 3 repeats are performed. Pick the correct statement(s).
The total number of runs is 15
The total number of degrees of freedom is 14
The degrees of freedom due to error is 10
The number of degrees of freedom due to treatment is 4
10. In Analysis of variance, the following is/are applicable in a 2³ factorial design experiment
There are three binary i.e. two-factor interaction terms
The mean square error is based on the unrepeated four corner points of the factorial design
The F-value is determined based on the ratio of mean square factors to mean square error
The denominator degrees of freedom used in the F-test is equal to that for pure error