# Probability and Statistics Questions and Answers – Sampling Distribution – 2

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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) NCn
b) nCN
c) 2n
d) 2N

Explanation: The number of ways of selecting and samples of size n from a population containing N atoms is NCn. The probability of selecting of each sample is 1/NCn.

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

Explanation: The number of ways of selecting n samples from a population containing n items is NCn. The population is N = 8 and sample size is n = 2. Therefore the number of possible samples are 8C2 = 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

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 NCn that is 6C2 = 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) nN
c) NCn
d) Nn

Explanation: The number of samples containing n items selected from a population of N items is Nn. The probability of selection of each sample is 1/Nn.

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

Explanation: The number of samples formed with n items from a population containing N items is Nn.
Here N = 6 and n = 2.
Hence samples are Nn = 62 = 36.

6. Find the sampling fraction where N is population size and n is the sample size?
a) n/N
b) NCn
c) nN
d) Nn

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

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

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

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

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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