وَأَحْصَىٰ كُلَّ شَيْءٍ عَدَدًا
"And He has enumerated everything in numbers." (Allah perfectly counts and knows the exact measure of all creations).
Q1. It includes a limited number of sampling units:
A. Finite population ✓ Correct Answer
B. Infinite population
C. Uncountable infinite
D. None
Explanation: A population with a fixed, countable number of sampling
units is a finite population.
Q2. It includes unlimited number of sampling units:
A. Finite population
B. Infinite population ✓ Correct Answer
C. Countable infinite
D. None
Explanation: A population with no fixed limit on the number of units
is an infinite population.
Q3. The numerical quantities that describe
probability distributions are called:
A. Estimate
B. Statistic
C. Estimator
D. Parameters ✓ Correct Answer
Explanation: Parameters are the fixed numerical characteristics that
describe a probability distribution (e.g. μ, σ²).
Q4. The population must be defined in terms of:
A. Content
B. Unit
C. Extent and time
D. All ✓ Correct Answer
Explanation: A population definition requires specifying its content,
sampling unit, and extent/time — all three.
Q5. The result obtained by rolling of a die:
A. Finite population
B. Infinite population ✓ Correct Answer
C. Limited population
D. None
Explanation: Since a die can be rolled repeatedly without limit, the
population of possible outcomes is considered infinite (a hypothetical
population).
Q6. Population of the heights of students enrolled at
a college in a given year is:
A. Unlimited
B. Finite ✓ Correct Answer
C. Infinite
D. None
Explanation: The number of students enrolled in a given year is fixed
and countable, so this is a finite population.
Q7. Procedure of selecting a representative sample
from population:
A. Sample
B. Sampling design
C. Sampling ✓ Correct Answer
D. None
Explanation: The overall procedure of drawing a representative sample
from a population is called sampling.
Q8. The collection of information from a part of
population:
A. Sample survey ✓ Correct Answer
B. Census
C. Complete enumeration
D. None
Explanation: Gathering data from only a part (sample) of the
population is called a sample survey.
Q9. A complete list of the sampling units:
A. Picture frame
B. Sample
C. Sampling frame ✓ Correct Answer
D. None
Explanation: A complete listing of all sampling units in the
population is called the sampling frame.
Q10. The collection of information from all elements
in population is called:
A. Sample survey
B. Census
C. Complete enumeration
D. b and c ✓ Correct Answer
Explanation: Collecting data from every element of the population is
called a census, also known as complete enumeration — both terms mean the same
thing.
Q11. Sampling may be the only means available for
obtaining the desired information if:
A. Population is destructive
B. Population is finite
C. Population is infinite
D. a and c ✓ Correct Answer
Explanation: When testing destroys the item (destructive population)
or the population is infinite, sampling is the only practical option — so both
(a) and (c) apply.
Q12. Random sampling provides more reliable estimates
than non-random sampling.
A. False
B. True ✓ Correct Answer
C. Unexplained
D. None
Explanation: Random sampling reduces selection bias and generally
provides more reliable, representative estimates.
Q13. Sample size may be greater than the population
size:
A. Without replacement
B. With replacement ✓ Correct Answer
C. All at a time selection
D. None
Explanation: With replacement, units can be reselected, so it's
possible to draw a sample larger than the population itself.
Q14. A sampling unit might be selected more than once
in selection:
A. Without replacement
B. With replacement ✓ Correct Answer
C. All at a time selection
D. None
Explanation: In sampling with replacement, each selected unit is
returned before the next draw, so it can be picked again.
Q15. Selected object is returned to the population
prior to subsequent selection:
A. Without replacement
B. With replacement ✓ Correct Answer
C. All at a time selection
D. None
Explanation: Returning the selected unit to the population before the
next draw is exactly how sampling with replacement works.
Q16. A finite population becomes infinite in
selection:
A. Without replacement
B. With replacement ✓ Correct Answer
C. All at a time selection
D. None
Explanation: Because units can be drawn repeatedly without limit,
sampling with replacement effectively makes even a finite population act as
infinite.
Q17. Which is true for sampling with replacement?
A. Sample size may be greater
than population size
B. Population becomes infinite
C. A unit can be selected more
than once
D. All ✓ Correct Answer
Explanation: All three statements correctly describe properties of sampling
with replacement.
Q18. If sampling is done with replacement, number of
possible samples is:
A. Nⁿ ✓ Correct Answer
B. ᴺCₙ
C. ᴺPₙ
D. None
Explanation: With replacement, each of the n draws has N choices
independently, giving Nⁿ possible samples.
Q19. The number of units available for the next
drawing does not change in a random sampling:
A. Without replacement
B. With replacement ✓ Correct Answer
C. All at a time selection
D. None
Explanation: Since the selected unit is returned, the population size
available for the next draw stays the same — this is sampling with replacement.
Q20. A sampling unit can't be selected more than
once:
A. All a time selection
B. Without replacement
selection ✓ Correct Answer
C. With replacement selection
D. None
Explanation: In sampling without replacement, once a unit is drawn it
is not returned, so it cannot be selected again.
Q21. Which is true for sampling without replacement?
A. Sample size may be greater
than population size
B. Population becomes infinite
C. A unit can't be selected
more than once ✓ Correct Answer
D. All
Explanation: Without replacement, units are not returned, so a unit
can never be selected more than once.
Q22. If sampling is done without replacement, number
of possible samples is:
A. Nⁿ
B. ᴺCₙ
C. ᴺPₙ ✓ Correct Answer
D. None
Explanation: Without replacement, ordered selection of n units out of
N gives ᴺPₙ possible samples.
Q23. A sampling unit can't be selected more than
once:
A. All a time selection
B. With replacement selection
C. Without replacement selection
D. a and c ✓ Correct Answer
Explanation: This holds under 'all at a time' selection and under
without-replacement selection, since neither allows repeat picks — so (a) and
(c).
Q24. The number of units remaining for each drawing
will be reduced by one:
A. Without replacement ✓ Correct Answer
B. With replacement
C. All at a time selection
D. None
Explanation: Since units are not returned, each draw without
replacement reduces the remaining pool by exactly one unit.
Q25. Every unit has equal probability of being drawn:
A. Simple random sampling
B. Random sampling
C. Unrestricted random sample
D. a and b ✓ Correct Answer
Explanation: Both simple random sampling and random sampling in
general give every unit an equal chance of selection.
Q26. The plural of stratum is:
A. Stratas
B. Strata ✓ Correct Answer
C. Stratums
D. Stratee
Explanation: The correct plural of the Latin-derived word 'stratum' is
'strata'.
Q27. The process of dividing a heterogeneous
population into homogeneous subgroup is called:
A. Stratification ✓ Correct Answer
B. Sampling
C. Ranking
D. None
Explanation: Splitting a mixed (heterogeneous) population into similar
(homogeneous) subgroups is called stratification.
Q28. Sampling distribution is probability
distribution of:
A. Parameter
B. Statistic ✓ Correct Answer
C. True value
D. None
Explanation: A sampling distribution describes the probability
distribution of a sample statistic across repeated samples.
Q29. Probability distribution of a sample statistic
is called:
A. Time series
B. Frequency distribution
C. Sampling
distribution ✓ Correct Answer
D. None
Explanation: By definition, this is called the sampling distribution
of the statistic.
Q30. Difference between value of statistic and
corresponding population parameter:
A. Sampling errors ✓ Correct Answer
B. Bias
C. Non-sampling errors
D. Non-random errors
Explanation: This specific discrepancy, arising purely because a
sample rather than the whole population was used, is called sampling error.
Q31. The difference between the sample results and
true value:
A. Error
B. Accuracy
C. Sampling error ✓ Correct Answer
D. All
Explanation: The deviation between what a sample shows and the true
population value is termed sampling error.
Q32. Sampling errors can be reduced:
A. By increasing the sample size
B. By improving the sampling
design
C. By using supplementary
information
D. All ✓ Correct Answer
Explanation: All of these approaches — larger samples, better design,
and extra information — help reduce sampling error.
Q33. Non sampling errors arise due to:
A. Response bias
B. Error in collecting data
C. Error in analysis data
D. All ✓ Correct Answer
Explanation: Non-sampling errors can stem from response bias, data
collection mistakes, and analysis errors alike.
Q34. Accuracy can be increased:
A. By increasing the sample size
B. Elimination of technical
errors
C. With increase in bias
D. a and b ✓ Correct Answer
Explanation: Accuracy improves with a larger sample size and by
removing technical errors — increasing bias would actually hurt accuracy.
Q35. The difference between expected value of
statistic and the true value of parameter:
A. Error
B. Bias ✓ Correct Answer
C. Sampling errors
D. a and b
Explanation: By definition, Bias = E(statistic) - true parameter
value.
Q36. Bias is:
A. Cumulative ✓ Correct Answer
B. De-cumulative
C. Decreasing
D. None
Explanation: Unlike sampling error (which tends to average out), bias
is cumulative — it doesn't cancel over repeated samples.
Q37. The errors caused by sampling the wrong
population of interest are called:
A. Sampling errors
B. Non-sampling errors
C. Non-random errors
D. b & c ✓ Correct Answer
Explanation: Sampling the wrong target population is a design flaw,
classified as both a non-sampling error and a non-random error.
Q38. These errors are present in census and sample
surveys:
A. Non sampling errors
B. Non random errors
C. Sampling errors
D. a and b ✓ Correct Answer
Explanation: Non-sampling (non-random) errors can occur in both a full
census and a sample survey, unlike sampling error which only occurs in samples.
Q39. The difference between the expected value of a
statistic and the population parameter:
A. Sampling error
B. Bias ✓ Correct Answer
C. Non-sampling error
D. Non random error
Explanation: This is precisely the definition of bias.
Q40. If 'T' be the sample statistic and 'θ' be the
parameter then Bias =
A. T - θ
B. θ - T
C. E(T) - θ ✓ Correct Answer
D. None
Explanation: Bias is defined as the expected value of the statistic
minus the true parameter: E(T) - θ.
Q41. Bias is a:
A. Systematic component of error
B. Cummulative
C. Decreases as sample size
increases
D. a and b ✓ Correct Answer
Explanation: Bias is a systematic (non-random) component of error, and
it is cumulative in nature.
Q42. By increasing the sample size, bias:
A. Increases
B. Decreases
C. Doesn't change ✓ Correct Answer
D. None
Explanation: Bias is a systematic error unrelated to sample size, so
increasing the sample size does not reduce it.
Q43. A sample which is free from bias:
A. Unbiased sample
B. Random sample
C. Non-probability sample
D. a and b ✓ Correct Answer
Explanation: A sample free from bias is generally called an unbiased
sample, and randomization (random sample) helps achieve this.
Q44. The standard error can be reduced:
A. By increasing the sample size
B. By improving the sampling
design
C. By using the supplementary
information
D. All ✓ Correct Answer
Explanation: All of these methods help lower the standard error of an
estimate.
Q45. Every random sample is a simple random sample.
A. False ✓ Correct Answer
B. True
C. Unexplained
D. None
Explanation: Random sampling is a broad category; simple random
sampling is just one specific type, so this statement is false.
Q46. A statistic:
A. Function of sample
observations
B. Doesn't contain unknown
parameter
C. A random variable
D. All ✓ Correct Answer
Explanation: A statistic is a function of sample data, contains no
unknown parameters, and varies randomly from sample to sample — all three are
true.
Q47. Standard deviation of statistic:
A. Standard deviation
B. Mean deviation
C. Standard error ✓ Correct Answer
D. Quartile deviation
Explanation: The standard deviation of the sampling distribution of a
statistic is specifically termed the standard error.
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