Multiple choice questions on chi-square distribution( statistical techniques-III) for AKTU Examination

 Here In this post we will discuss the important questions of the Sample distribution of statistical techniques-III  . These questions will help you in your mid semesters exams or the semester exams or any other competitive exams. And this will also help in your upcoming  AKTU semester exam.

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1. Consider a set of 18 samples from a standard normal distribution. We square each sample and sum all the squares. The number of degrees of freedom for a Chi Square distribution will be?

a) 17

b) 18

c) 19

d) 20   

Answer: b

Explanation: In Chi Square Distribution the number of standard normal derivatives or samples equals the number of degrees of freedom.

Here total number of standard normal derivatives = 18.

Hence the number of degrees of freedom for a Chi Square distribution = 18.

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2. What is the mean of a Chi Square distribution with 6 degrees of freedom?

a) 4

b) 12

c) 6

d) 8   

Answer: c

Explanation: By the property of Chi Square distribution, the mean corresponds to the number of degrees of freedom.

Degrees of freedom = 6.

Hence mean = 6.

3. Which Chi Square distribution looks the most like a normal distribution?

a) A Chi Square distribution with 4 degrees of freedom

b) A Chi Square distribution with 5 degrees of freedom

c) A Chi Square distribution with 6 degrees of freedom

d) A Chi Square distribution with 16 degrees of freedom

 Answer: c

Explanation: When the number of degrees of freedom in Chi Square distribution increases it tends to correspond to normal distribution. The option with a maximum number of degrees of freedom is 16.

4. A bag contains 80 chocolates. This bag has 4 different colors of chocolates in it. If all four colors of chocolates were equally likely to be put in the bag, what would be the expected number of chocolates of each color?

a) 12

b) 11

c) 20

d) 9

Answer: c

Explanation: If all four colors were equally likely to be put in the bag, then the expected frequency for a given color would be 1/4th of the chocolates.

N = 80, r = 1/4

So, the expected frequency = N*r = (1/4)*(80) = 20.

5. The Variance of Chi Squared distribution is given as k.

a) True

b) False

 Answer: b

Explanation: The Mean of Chi Squared distribution is given as k. The Variance of Chi Squared distribution is given as 2k.

6. Which of these distributions is used for a testing hypothesis?

a) Normal Distribution

b) Chi-Squared Distribution

c) Gamma Distribution

d) Poisson Distribution

Answer: b

Explanation: Chi-Squared Distribution is used for testing hypothesis. The value of X2 decides whether the hypothesis is accepted or not.

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