# Probability and Statistics Questions and Answers – Sampling Distribution of Means

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This set of Probability and Statistics Questions and Answers for Entrance exams focuses on “Sampling Distribution of Means”.

1. If the mean of population is 29 then the mean of sampling distribution is __________
a) 29
b) 30
c) 21
d) 31

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.

2. 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

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.

3. 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

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.
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4. If the standard deviation of a population is 50 and the sample size is 16 then the standard deviation of the sampling distribution is ________
a) 11.25
b) 12.25
c) 13.25
d) 14.25

Explanation: The standard deviation of a population ϕ is given as σ/(n)1/2 where n is the sample size and σ is the standard deviation of population.
Substituting the values of n=16 and σ=50.
σ/(n)1/2
50/(16)1/2
we get ϕ=12.25.

5. In sampling distribution what does the parameter k represents ________
a) Sub stage interval
b) Secondary interval
c) Multi stage interval
d) Sampling interval

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

6. 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

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.

7. The cluster sampling, stratified sampling or systematic samplings are types of ________
a) direct sampling
b) indirect sampling
c) random sampling
d) non random sampling

Explanation: The cluster sampling, stratified sampling or systematic samplings are types of random sampling. The advantage of probability sampling methods is that they ensure that the sample chosen is representative of the population.

8. Which of the following is classified as unknown or exact value that represents the whole population?
a) predictor
b) guider
c) parameter
d) estimator

Explanation: The unknown or exact value that represents the whole population is called as parameter. Generally parameters are defined by small Roman symbols.

9. 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

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.

10. The selected clusters in a clustering sampling are known as ________
a) elementary units
b) primary units
c) secondary units
d) proportional units

Explanation: In Cluster the population is divided into various groups called as clusters. The selected clusters in a sample are called as elementary units.

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