This set of Probability and Statistics Interview Questions and Answers focuses on “Sampling Distribution – 2”.

1. A population has N items. Samples of size n are selected without replacement. Find the number of possible samples.

a) ^{N}C_{n}

b) ^{n}C_{N}

c) 2^{n}

d) 2^{N}

View Answer

Explanation: The number of ways of selecting and samples of size n from a population containing N atoms is

^{N}C

_{n}. The probability of selecting of each sample is 1/

^{N}C

_{n}.

2. Find the number of all possible samples from a population containing 8 items from which 2 items are selected at random without replacement.

a) 56

b) 28

c) 66

d) 38

View Answer

Explanation: The number of ways of selecting n samples from a population containing n items is

^{N}C

_{n}. The population is N = 8 and sample size is n = 2. Therefore the number of possible samples are

^{8}C

_{2}= 28.

3. A bag contains 6 balls of different colours. A student selects 2 balls at random without replacement. Find all possible combinations of the colours of the selected balls.

a) 13

b) 14

c) 15

d) 16

View Answer

Explanation: Considering the experiment to be a sampling distribution where the population contains 6 balls and each sample contains 2 balls. The number of possible samples are

^{N}C

_{n}that is

^{6}C

_{2}= 15 samples.

4. Consider a population containing N items and n are selected as a sample with replacement. Find all the possible samples.

a) N

b) n^{N}

c) ^{N}C_{n}

d) N^{n}

View Answer

Explanation: The number of samples containing n items selected from a population of N items is N

^{n}. The probability of selection of each sample is 1/N

^{n}.

5. A bag contains 6 pairs of socks. If 2 pairs of socks are selected at random with replacement then the number of possible samples is?

a) 6

b) 12

c) 36

d) 216

View Answer

Explanation: The number of samples formed with n items from a population containing N items is N

^{n}.

Here N = 6 and n = 2.

Hence samples are N

^{n}= 6

^{2}= 36.

6. Find the sampling fraction where N is population size and n is the sample size?

a) n/N

b) ^{N}C_{n}

c) n^{N}

d) N^{n}

View Answer

Explanation: In a sampling distribution if N is the population size, n is the sample size then number of sampling fractions is n/N.

7. In random sampling the probability of selecting an item from a population is unknown.

a) True

b) False

View Answer

Explanation: A random sample is defined as the sampling in which the probability off the selecting item from a population is known. Hence it is also called as Probability Sampling.

8. In a sampling distribution the population correction factor is given by?

a) (N-1/N-n)^{1/2}

b) (N-n/N-1)^{1/2}

c) (n-1/N-n)^{1/2}

d) (N-1/n-1)^{1/2}

View Answer

Explanation: The population correction factor is given by (N-n/N-1)

^{1/2}. When we sample the population for more than 5% without replacement we require the population correction factor.

9. A population has 10 items and a sample has been selected from it containing 5 items. Find the finite population correction factor.

a) (5/8)^{1/2}

b) (5/7)^{1/2}

c) (5/9)^{1/2}

d) (5/6)^{1/2}

View Answer

Explanation: The population correction factor is given by (N-n/N-1)

^{1/2}. Here N = 10 and n = 5

(N-n/N-1)

^{1/2}

(10-5/10-1)

^{1/2}

(5/9)

^{1/2}

which gives the value of correction factor as (5/9)

^{1/2}.

10. Find the value of standard error Ẋ in a sampling distribution with replacement. Given that standard deviation of the population of 16 items is 8.

a) 3

b) 4

c) 2

d) 5

View Answer

Explanation: Standard error in a sampling distribution with replacement is given by Ẋ = σ/(n)

^{1/2}. Hence n = 16 and σ = 8

Ẋ = σ/(n)

^{1/2}

Ẋ = 8/(16)

^{1/2}

which gives the value of Ẋ = 2.

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