This set of Probability and Statistics Questions and Answers for Campus interviews focuses on “Sampling Distribution of Proportions”.

1. The probability of selecting a sample containing n items from a population with N items without replacement in a Sampling Distribution is?

a) 1/^{N}C_{n}

b) 1/^{n}C_{N}

c) 1/2^{n}

d) 1/2^{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 18 items from which 6 items are selected at random without replacement.

a) 18564

b) 15864

c) 20264

d) 21564

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 = 18 and sample size is n = 6. Therefore the number of possible samples are

^{18}C

_{6}= 18564.

3. A pack of cards contains 52 cards. A player selects 4 cards at random without replacement. Find all possible combinations of the cards selected.

a) 207752

b) 270752

c) 270725

d) 207725

View Answer

Explanation: Considering the experiment to be a sampling distribution where the population contains 52 cards and each sample contains 4 cards. The number of possible samples without replacement are

^{N}C

_{n}that is

^{52}C

_{4}= 207725 samples.

4. A population contains N items out of which n items are selected with replacement. Find the probability of the sample being selected.

a) 1/N

b) 1/n^{N}

c) 1/^{N}C_{n}

d) 1/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 box contains 26 pairs of napkins. If 3 pairs of napkins are selected at random with a replacement then the number of possible samples is _______

a) 17675

b) 17566

c) 17576

d) 17556

View Answer

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

^{n}.

Here N = 26 and n = 3.

Hence samples are N

^{n}= 26

^{3}= 17576.

6. A sample was formed consisting of 8 students from a total of 56 students for certain task. Find the sampling fraction of the population of students.

a) 1/7

b) 7

c) 49

d) 1/49

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. Hence N=56 and n=8 which gives n/N as 8/56 = 1/7.

7. Find the population proportion p for an IPL team having total 30 players with 10 overseas players.

a) 1/2

b) 1/3

c) 2/3

d) 1/4

View Answer

Explanation: The population proportion p for a population consisting of N items with X specialized items is given as X/N. Now N=30, X=10. Hence p = X/N = 10/30 = 1/3.

8. It is provided that for a sampling distribution E(X)=11 and ϕ=13. Find the bias in the sampling.

a) 2

b) 4

c) 6

d) 3

View Answer

Explanation: The bias for sampling distribution is given as |E(X) – ϕ|.

|11 – 13| = 2

Hence bias is 2.

9. Find the standard error of population proportion p for sampling with replacement. The population proportion is 0.5 and size of sample is 4.

a) 0.5

b) 0.25

c) 0.225

d) 0.375

View Answer

Explanation: The standard error of population proportion in sampling distribution with replacement is given as [p*(1-p)/n]1/2. Here p=0.5 and n=4. Hence substituting the values we get

[0.5*(1-0.5)/4]1/2

= 0.25.

10. Find the value of standard error Ẋ in a sampling distribution without replacement. Given that the standard deviation of the population of 100 items is 25.

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}. The standard error with the replacement of items remains the same that is Ẋ = σ/(n)

^{1/2}.

Hence n = 100 and σ = 25

Ẋ = σ/(n)

^{1/2}

Ẋ = 25/(100)

^{1/2}

Ẋ = 2.5

The value of Ẋ = 2.5.

**Sanfoundry Global Education & Learning Series – Probability and Statistics.**

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