وَأَحْصَىٰ كُلَّ شَيْءٍ عَدَدًا
"And He has enumerated everything in numbers." (Allah perfectly counts and knows the exact measure of all creations).
Q1. A characteristic which varies in quality:
A. Attribute
B. Qualitative variable
C. Quantitative variable
D. a and b ✓ Correct Answer
Explanation: A characteristic that varies in quality (not measured
numerically) is called both an attribute and a qualitative variable.
Q2. It is obtained by noting presence or absence in
the objects:
A. Attribute
B. Qualitative variable
C. Quantitative variable
D. a and b ✓ Correct Answer
Explanation: Noting the presence or absence of a characteristic
defines an attribute, which is itself a type of qualitative variable.
Q3. The eye color of 100 men is:
A. Quantitative variable
B. Qualitative variable
C. Attribute
D. b and c ✓ Correct Answer
Explanation: Eye color is a non-numeric characteristic, making it both
a qualitative variable and an attribute.
Q4. A set of the objects which are sharing a given
characteristic is:
A. Class ✓ Correct Answer
B. Frequency
C. Total number of observation
D. None
Explanation: A group of objects sharing a common characteristic is
called a class.
Q5. The number of observations which are distributed
in a class is called:
A. Class
B. Frequency ✓ Correct Answer
C. Total number of observation
D. None
Explanation: The count of observations falling within a class is
called its frequency.
Q6. Classes represented by both positive and negative
attributes are called:
A. Positive classes
B. Negative classes
C. Contrary class ✓ Correct Answer
D. None
Explanation: A class defined by a mix of positive and negative
attributes (e.g. Aβ) is called a contrary class.
Q7. The process of dividing the objects into two
mutually exclusive classes is called:
A. Two way classification
B. Dichotomy
C. Four way classification
D. a and b ✓ Correct Answer
Explanation: Splitting objects into two mutually exclusive classes is
called both two-way classification and dichotomy.
Q8. Classes specified by two attributes are known as
the classes of order:
A. 0
B. 1
C. 2 ✓ Correct Answer
D. 3
Explanation: When classes are specified using two attributes together,
they are classes of order 2.
Q9. For k attributes the total number of class
frequencies would be:
A. 2ᵏ ✓ Correct Answer
B. 1ᵏ
C. 4ᵏ
D. 3ᵏ
Explanation: For k attributes, the total number of class frequencies
(of all orders combined) is 2ᵏ.
Q10. In study of attributes the frequencies of
classes of the highest order are called:
A. Ultimate frequencies ✓ Correct Answer
B. Simple frequencies
C. Marginal frequencies
D. None
Explanation: The frequencies of the highest-order classes (specified
by all attributes) are called ultimate frequencies.
Q11. In study of attributes the total number of
observations 'n' is the frequency of the class of order:
A. 0 ✓ Correct Answer
B. 1
C. 2
D. 3
Explanation: The total number of observations 'n' represents the
frequency of the class of order zero.
Q12. For k attributes the number of ultimate classes
is:
A. 2ᵏ ✓ Correct Answer
B. 1ᵏ
C. 4ᵏ
D. 3ᵏ
Explanation: For k attributes, the number of ultimate (highest order)
classes is 2ᵏ.
Q13. For 2 attributes the number of ultimate classes
is:
A. 4 ✓ Correct Answer
B. 1
C. 8
D. None
Explanation: For 2 attributes, the number of ultimate classes = 2² =
4.
Q14. In study of attributes, class frequencies are:
A. Enclosed in brackets ✓ Correct Answer
B. In bold letters
C. In Latin letters
D. None
Explanation: By convention, class frequencies in the study of
attributes are written enclosed in brackets, e.g. (AB).
Q15. (αB) denotes the number of objects possessing
attribute:
A. B but not A ✓ Correct Answer
B. A but not B
C. Both A and B
D. All
Explanation: The symbol α represents 'not A', so (αB) denotes objects
that possess B but not A.
Q16. In study of attributes no class frequency can
be:
A. Positive
B. Negative ✓ Correct Answer
C. Greater than 0
D. None
Explanation: A valid class frequency can never be negative, since it
represents a count of observations.
Q17. In study of attributes, if any class frequency
is negative, the data are:
A. Inconsistent ✓ Correct Answer
B. Consistent
C. Greater than 0
D. None
Explanation: A negative class frequency is impossible for real data,
indicating the data set is inconsistent.
Q18. In study of attributes the data are inconsistent
if:
A. All ultimate class frequencies
are positive
B. Any ultimate class
frequency is negative ✓ Correct Answer
C. The number of attributes are
more than two
D. None
Explanation: Data become inconsistent as soon as even one ultimate
class frequency turns out negative.
Q19. If no ultimate class frequency is negative, the
data would be:
A. Consistent ✓ Correct Answer
B. Inconsistent
C. Computational error
D. a & c
Explanation: When all ultimate class frequencies are non-negative, the
data set is considered consistent.
Q20. There is complete association between attribute
A and B if:
A. All A's are B's and all B's
are A's
B. All A's are B's ✓ Correct Answer
C. B's are A's
D. All
Explanation: Complete association between A and B means every A is
also a B, i.e. (αβ) = 0.
Q21. There is complete dissociation between attribute
A and B if:
A. All A's are B's and all B's
are A's
B. All A's are B's
C. B's are A's
D. None of A's is B's and
none of α's is β's ✓ Correct Answer
Explanation: Complete dissociation means A and B never occur together,
and their absences never occur together either.
Q22. Disassociation does not imply independence:
A. False
B. Unexplained
C. True ✓ Correct Answer
D. None
Explanation: This statement is true — attributes can be disassociated
(negatively related) without being statistically independent.
Q23. For two attributes A & B, (A), (B), (α), (β)
are frequencies of the classes of order:
A. 1 ✓ Correct Answer
B. 2
C. 3
D. None
Explanation: (A), (B), (α), and (β) are each specified by a single
attribute, making them classes of order 1.
Q24. For the consistence of a set of class
frequencies, no ultimate class frequency should be:
A. Negative ✓ Correct Answer
B. Positive
C. Zero
D. None
Explanation: Consistency of class frequencies requires that no
ultimate class frequency is negative.
Q25. The two attributes A and B are said to be
independent if (AB) =
A. (B)(B)/n
B. (A)(A)/n
C. (A)(B)/n ✓ Correct Answer
D. (A)/(B)
Explanation: Independence between A and B holds when the joint
frequency equals (A)(B)/n, mirroring the multiplication rule for independent
events.
Q26. (β) =
A. (A)+(α)
B. (B)+(β)
C. (Aβ)+(αβ) ✓ Correct Answer
D. (AB)+(αβ)
Explanation: (β) is split into those objects that are A but not B, and
those that are neither A nor B: (Aβ)+(αβ).
Q27. Yule's coefficient of association lies between:
A. 0 to +1
B. -1 to 1 ✓ Correct Answer
C. -1 to 0
D. None
Explanation: Yule's coefficient of association (Q) ranges from -1 to
+1.
Q28. If Yule's coefficient of association Q = 1, then
two attributes are:
A. Independent
B. Completely
associated ✓ Correct Answer
C. Completely disassociated
D. None
Explanation: A value of Q = 1 indicates that the two attributes are
completely (perfectly) associated.
Q29. If Yule's coefficient of association Q = -1,
then two attributes are:
A. Independent
B. Completely associated
C. Completely
disassociated ✓ Correct Answer
D. None
Explanation: A value of Q = -1 indicates that the two attributes are
completely disassociated.
Q30. The χ² distribution is:
A. Discrete
B. Continuous ✓ Correct Answer
C. Discontinuous
D. Undefined
Explanation: The chi-square (χ²) distribution is a continuous probability
distribution.
Q31. The value of chi-square (χ²) is always:
A. Negative
B. Positive ✓ Correct Answer
C. Zero
D. Undefined
Explanation: Since χ² is a sum of squared standardized deviations, it
is always non-negative (positive).
Q32. The random variable χ² can assume values:
A. -∞ to 0
B. -∞ to ∞
C. 0 to ∞ ✓ Correct Answer
D. None
Explanation: The chi-square random variable ranges from 0 to infinity,
since it can never be negative.
Q33. The parameter(s) of the chi-square distribution
is (are):
A. Degrees of freedom ✓ Correct Answer
B. n-1
C. Mean and variance
D. None
Explanation: The chi-square distribution is characterized entirely by
its degrees of freedom.
Q34. The parameter(s) of the chi-square distribution
is (are):
A. Two
B. One ✓ Correct Answer
C. Three
D. Unlimited
Explanation: The chi-square distribution has exactly one parameter:
its degrees of freedom.
Q35. The relation Z² = χ² between standard normal and
chi-square holds for:
A. Single degrees of
freedom ✓ Correct Answer
B. Two degrees of freedom
C. Three degrees of freedom
D. More than three degrees of
freedom
Explanation: The square of a single standard normal variable follows a
chi-square distribution with 1 degree of freedom.
Q36. For the better approximation of χ², each
expected cell frequency should be:
A. Less than 5
B. At least 5 ✓ Correct Answer
C. Zero
D. None
Explanation: For the chi-square approximation to be valid, each
expected cell frequency should be at least 5.
Q37. For one degree of freedom, the relationship
between standard normal and chi-square variable is:
A. √χ² = Z
B. Z² = ∛χ²
C. Z = χ²
D. Z² = χ² ✓ Correct Answer
Explanation: With 1 degree of freedom, the square of the standard
normal variable equals the chi-square variable: Z² = χ².
Q38. In χ²-test for independence, the critical region
locates:
A. Right tail only ✓ Correct Answer
B. Left tail only
C. Both tails
D. No critical region
Explanation: For the chi-square test of independence, the critical
(rejection) region is located only in the right tail.
Q39. In testing of independence of attributes, the
critical region is:
A. χ²cal ≤ χ²table
B. χ²cal < χ²table
C. χ²cal > χ²table ✓ Correct Answer
D. None
Explanation: The critical (rejection) region is where the calculated
chi-square exceeds the table value: χ²cal > χ²table.
Q40. In testing of independence of attributes, null
hypothesis is accepted when:
A. χ²cal ≤ χ²table ✓ Correct Answer
B. χ²cal < χ²table
C. χ²cal > χ²table
D. None
Explanation: The null hypothesis of independence is accepted when the
calculated chi-square is less than or equal to the table value.
Q41. In testing of independence of attributes, null
hypothesis is rejected when:
A. χ²cal ≤ χ²table
B. χ²cal < χ²table
C. χ²cal > χ²table ✓ Correct Answer
D. None
Explanation: The null hypothesis is rejected when the calculated
chi-square exceeds the table value.
Q42. If χ²cal < χ²table then attributes are:
A. Not associated ✓ Correct Answer
B. Dependent
C. Associated
D. None
Explanation: When the calculated value is less than the table value,
we fail to reject independence, so the attributes are not associated.
Q43. Greater the value of χ²:
A. More chance of rejecting
H₀ ✓ Correct Answer
B. More chance of rejecting H₁
C. More chance of accepting H₀
D. No decision
Explanation: A larger chi-square value pushes further into the
critical region, increasing the chance of rejecting the null hypothesis (H₀).
Q44. Coefficient of contingency applied when:
A. H₀ is rejected ✓ Correct Answer
B. H₁ is rejected
C. H₀ is not rejected
D. None
Explanation: The coefficient of contingency is used to measure the
strength of association once H₀ (independence) has been rejected.
Q45. For test of independence of r x c contingency
table, degrees of freedom are:
A. (r-1)(c-1) ✓ Correct Answer
B. (r+1)(c+1)
C. (r+1)(c-1)
D. (1-r)(1-c)
Explanation: For an r × c contingency table, the degrees of freedom
for the independence test are (r-1)(c-1).
Q46. A contingency table is made up of the observed
frequencies relative to the:
A. Two attributes ✓ Correct Answer
B. Three attributes
C. Four attributes
D. None
Explanation: A contingency table classifies observed frequencies
according to two attributes simultaneously.
Q47. To test the independence of attributes we use:
A. Z-test
B. F-test
C. t-test
D. χ²-test ✓ Correct Answer
Explanation: The chi-square (χ²) test is the standard test used to
check independence between attributes.
Q48. Rank correlation is used in case of:
A. Ratio scale
B. Interval scale
C. Nominal scale
D. Ordinal scale ✓ Correct Answer
Explanation: Rank correlation is designed for ordinal (ranked) data,
where only the order of values matters.
Q49. Rank correlation is used when relationship
between variables is:
A. Linear
B. Perfect linear
C. Non-linear ✓ Correct Answer
D. None
Explanation: Rank correlation is especially useful when the
relationship between variables is non-linear, since it depends only on ranks.
Q50. The value of rank correlation coefficient lies
between:
A. 0 to 1
B. -1 to 0
C. -1 to +1 ✓ Correct Answer
D. 0 to ∞
Explanation: Like other correlation coefficients, the rank correlation
coefficient ranges from -1 to +1.
Q51. The value of rank correlation coefficient is -2:
A. Correct
B. There may be a
computational error ✓ Correct Answer
C. Perfect negative correlation
D. No correlation
Explanation: Since rank correlation must lie between -1 and +1, a
value of -2 is impossible and indicates a computational error.
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