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
View Answer

Answer: a
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.
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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

Answer: b
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
View Answer

Answer: c
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
View Answer

Answer: d
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
View Answer

Answer: c
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.
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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
View Answer

Answer: a
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

Answer: b
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

Answer: b
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

Answer: c
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

Answer: c
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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn