# Multiple choice questions on Sampling Distribution 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**. What does the central limit theorem state?

a) if the sample size increases sampling distribution must approach normal distribution

b) if the sample size decreases then the sample distribution must approach normal distribution

c) if the sample size increases then the sampling distribution much approach an exponential distribution

d) if the sample size decreases then the sampling distribution much approach an exponential distribution

Answer: a

Explanation: The central limit theorem states that if the sample size increases sampling distribution must approach normal distribution. Generally a sample size more than 30 us considered as large enough.

**2**. Standard error is always non- negative.

a) True

b) False

Answer: a

Explanation: When we square the mean for standard deviations any negative value becomes positive. The addition of all the positive values results in a positive value. Then the square root of the positive value is also positive. Hence all standard deviations are non-negative.

3. Sampling error increases as we increase the sampling size.

a) True

b) False

Answer: b

Explanation: Sampling error is inversely proportional to the sampling size. As the sampling size increases the sampling error decreases.

4. The difference between the sample value expected and the estimates value of the parameter is called as?

a) bias

b) error

c) contradiction

d) difference

Answer: a

Explanation: The difference between the expected sample value and the estimated value of parameter is called as bias. A sample used to estimate a parameter is unbiased if the mean of its sampling distribution is exactly equal to the true value of the parameter being estimated.

5. Which of the following is a subset of population?

a) distribution

b) sample

c) data

d) set

Answer: b

Explanation: In sampling distribution we take a subset of population which is called as a sample. The main advantage of this sample is to reduce the variability present in the statistics.

6. The sampling error is defined as?

a) difference between population and parameter

b) difference between sample and parameter

c) difference between population and sample

d) difference between parameter and sample

Answer: c

Explanation: In sampling distribution the sampling error is defined as the difference between population and the sample. Sampling error can be reduced by increasing the sample size.

7. Any population which we want to study is referred as?

a) standard population

b) final population

c) infinite population

d) target population

Answer: d

Explanation: In sampling distribution we take a part of a population under study which is called as target population. Target population is also called as a sample.

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

a) 1/NCn

b) 1/nCN

c) 1/2n

d) 1/2N

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.

9. 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

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.

10. 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

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.

11. 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

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.

12. 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

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.

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

a) n/N

b) NCn

c) nN

d)Nn

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.

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

a) True

b) False

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.

15. 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

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.

16. If the mean of population is 29 then the mean of sampling distribution is __________

a) 29

b) 30

c) 21

d) 31

Answer: a

Explanation: In a sampling distribution the mean of the population is equal to the mean of the sampling distribution. Hence mean of population=29. Hence mean of sampling distribution=29.

17. In systematic sampling, population is 240 and selected sample size is 60 then sampling interval is ________

a) 240

b) 60

c) 4

d) 0.25

Answer: c

Explanation: Sampling interval is defined as the interval in which the population is divided. The sampling interval is given as the population/sample size = 240/60 = 4.

18. The method of selecting a desirable portion from a population which describes the characteristics of whole population is called as ________

a) sampling

b) segregating

c) dividing

d) implanting

Answer: a

Explanation: The method of selecting a desirable portion from a population which describes the characteristics of whole population is called as Sampling. It is useful in combining the related samples and hence making the distribution easy to manipulate.

19. In sampling distribution what does the parameter k represents ________

a) Sub stage interval

b) Secondary interval

c) Multi stage interval

d) Sampling interval

Answer: d

Explanation: In sampling distribution the parameter k represents Sampling interval. It represents the distance between which data is taken.

20. If the distribution of sample and population changes then the mean of Sampling distribution must be equal to ________

a) standard deviation of population

b) variance of population

c) sample of population

d) mean of population

Answer: d

Explanation: In a sampling distribution irrespective of the variation in sample and population the mean of the population is equal to the mean of the sampling distribution. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ.

21. A sample size is considered large in which of the following cases?

a) n > or = 30

b) n > or = 50

c) n < or = 30

d) n < or = 50

Answer: a

Explanation: Generally a sample having 30 or more sample values is called a large sample. By the Central Limit Theorem such a sample follows a Normal Distribution.

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

a) 1/NCn

b) 1/nCN

c) 1/2n

d) 1/2N

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.

23. 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

Answer: a

Explanation: The number of ways of selecting n samples from a population containing n items is NCn. The population is N = 18 and sample size is n = 6. Therefore the number of possible samples are 18C6 = 18564.

24. 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

Answer: c

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 NCn that is 52C4 = 207725 samples.

25. 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/nN

c) 1/NCn

d) 1/Nn

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.

26. 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

Answer: c

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

Here N = 26 and n = 3.

Hence samples are Nn = 263 = 17576.

27. 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

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

28. 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

Answer: b

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.