# Probability and Statistics Questions and Answers – Sampling Distribution – 1

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This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on “Sampling Distribution – 1”.

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

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

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

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
d) difference

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. In which of the following types of sampling the information is carried out under the opinion of an expert?
a) quota sampling
b) convenience sampling
c) purposive sampling
d) judgement sampling

Explanation: In judgement sampling is carried under an opinion of an expert. The judgement sampling often results in a bias because of the variance in the expert opinion.

6. Which of the following is a subset of population?
a) distribution
b) sample
c) data
d) set

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.

7. 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

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.

8. Any population which we want to study is referred as?
a) standard population
b) final population
c) infinite population
d) target population

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.

9. Suppose we want to make a voters list for the general elections 2019 then we require __________
a) sampling error
b) random error
c) census
d) simple error

Explanation: Study of population is called a Census. Hence for making a voter list for the general elections 2019 we require Census.

10. Selection of a football team for FIFA World Cup is called as?
a) random sampling
b) systematic sampling
c) purposive sampling
d) cluster sampling

Explanation: A purposive sampling is defined as the sampling done on the basis of the characteristics of the population. Hence selecting a football team for the FIFA World cup is a purposive sampling.

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