وَأَحْصَىٰ كُلَّ شَيْءٍ عَدَدًا
"And He has enumerated everything in numbers." (Allah perfectly counts and knows the exact measure of all creations).
Q1. Statistical hypothesis is an assertion about the
nature of:
A. Population ✓ Correct Answer
B. Sample
C. Statistic
D. None
Explanation: A statistical hypothesis is an assertion or conjecture
about a characteristic of the population.
Q2. Statement made about the population parameter is
called:
A. Statistical
hypothesis ✓ Correct Answer
B. Estimation
C. Point estimation
D. None
Explanation: A claim or assertion about a population parameter is
called a statistical hypothesis.
Q3. Statistical hypothesis is an assertion about the
nature of:
A. Sample
B. Population ✓ Correct Answer
C. Statistic
D. None
Explanation: A statistical hypothesis concerns the population, not the
sample or a sample statistic.
Q4. Hypotheses are usually phrased quantitatively in
terms of:
A. Population parameter ✓ Correct Answer
B. Statistic
C. Estimator
D. None
Explanation: Hypotheses are stated quantitatively about population
parameters, such as μ or p.
Q5. A test of hypothesis is always about:
A. A test statistic
B. A sample statistic
C. Population parameter ✓ Correct Answer
D. None
Explanation: The purpose of hypothesis testing is to draw a conclusion
about a population parameter.
Q6. “The given coin is unbiased” is:
A. H₀ ✓ Correct Answer
B. H₁
C. (a) & (b)
D. None
Explanation: A claim of “no difference” or status quo, like an
unbiased coin, is stated as the null hypothesis H₀.
Q7. “A drug is ineffective in curing a particular
disease” is:
A. H₀
B. H₁
C. Research hypothesis
D. (a) & (c) ✓ Correct Answer
Explanation: The statement being directly tested (the drug's
ineffectiveness) serves as both the null hypothesis and the research hypothesis
under investigation.
Q8. The names of one tailed and two tailed tests are
associated with:
A. Null hypothesis
B. Alternative hypothesis ✓ Correct Answer
C. Research hypothesis
D. None
Explanation: Whether a test is one-tailed or two-tailed is determined
by the direction specified in the alternative hypothesis.
Q9. The sign in the alternative hypothesis in a
left-tailed test is always:
A. < ✓ Correct Answer
B. >
C. =
D. ≠
Explanation: A left-tailed test's alternative hypothesis always uses
the 'less than' (<) sign.
Q10. Which sign is used in making of alternative
hypothesis?
A. ≥
B. ≤
C. =
D. None ✓ Correct Answer
Explanation: The alternative hypothesis uses only <, >, or ≠ —
never ≥, ≤, or =, so the answer is none of these.
Q11. Which sign is not used in making of null
hypothesis?
A. <
B. >
C. ≠
D. All ✓ Correct Answer
Explanation: The null hypothesis is always stated with an equality (=)
sign, so none of <, >, or ≠ are used — hence all of them.
Q12. A two tailed test is a test with:
A. Two rejection
regions ✓ Correct Answer
B. No rejection regions
C. Two test statistics
D. None
Explanation: A two-tailed test has rejection regions in both tails of
the distribution.
Q13. If μ ≠ 60 then test is called:
A. One tailed test
B. Two tailed test ✓ Correct Answer
C. (a) & (b)
D. None
Explanation: A not-equal-to (≠) alternative hypothesis always
indicates a two-tailed test.
Q14. α is the probability of making a:
A. Type-I error ✓ Correct Answer
B. Type-II error
C. Type-III error
D. Type-IV error
Explanation: α (the significance level) is defined as the probability
of committing a Type-I error.
Q15. In testing the hypothesis about the mean of a
population, we will use the Z distribution:
A. When population is normal and
σ² is known
B. The sample size is
sufficiently large
C. (a) & (b) ✓ Correct Answer
D. None
Explanation: The Z-test is used either when the population is normal
with known variance, or when the sample size is large enough — both conditions
apply.
Q16. t-distribution is used when:
A. Population is normal
B. σ² is unknown
C. Sample size is small
D. All ✓ Correct Answer
Explanation: The t-distribution is used when the population is normal,
the variance is unknown, and the sample size is small — all conditions
together.
Q17. H₀ will be accepted or rejected depending upon
the calculated value of:
A. Test statistic ✓ Correct Answer
B. Parameter
C. (a) & (b)
D. None
Explanation: The decision to accept or reject H₀ is based on the
calculated value of the test statistic.
Q18. If β is the probability of Type-II error, then
the power of test is denoted by:
A. 1-α
B. α+β
C. 1-β ✓ Correct Answer
D. α-β
Explanation: The power of a test is defined as 1-β, the probability of
correctly rejecting a false null hypothesis.
Q19. The values of test statistic that are either too
large or too small to be consistent with the hypothesis define a:
A. One tailed test
B. Two tailed test ✓ Correct Answer
C. (a) & (b)
D. None
Explanation: When both extremely large and extremely small values lead
to rejection, this describes a two-tailed test.
Q20. The values of test statistic that are too large
to be consistent with the hypothesis define a:
A. Left tailed test
B. Two tailed test
C. Right tailed test ✓ Correct Answer
D. None
Explanation: When only unusually large test statistic values lead to
rejection, this is a right-tailed test.
Q21. The analyst is concerned with detecting values
of the test statistic that are too small to be consistent with the hypothesis
being tested. This is a:
A. Right tailed test
B. Two tailed test
C. Left tailed test ✓ Correct Answer
D. None
Explanation: Focusing on unusually small test statistic values
corresponds to a left-tailed test.
Q22. Two tailed test is designed to test the values
of test statistic that are:
A. Too large to be consistent
B. Too small to be consistent
C. Either too small or too
large to be consistent ✓ Correct Answer
D. None
Explanation: A two-tailed test flags values that are either too large
or too small to be consistent with the null hypothesis.
Q23. A one tailed test is a test with:
A. One rejection region ✓ Correct Answer
B. Two rejection regions
C. Two test statistics
D. None
Explanation: A one-tailed test has only a single rejection region,
located in one tail of the distribution.
Q24. Type-I error is committed when:
A. A null hypothesis is not
rejected when it's actually false
B. A null hypothesis is
rejected when it's actually true ✓
Correct Answer
C. An alternative hypothesis is
rejected when it's actually false
D. None
Explanation: Type-I error occurs when a true null hypothesis is
incorrectly rejected.
Q25. Type-II error is committed when:
A. A null hypothesis is not
rejected when it's actually false ✓
Correct Answer
B. A null hypothesis is rejected
when it's actually false
C. An alternative hypothesis is
rejected when it's actually false
D. None
Explanation: Type-II error occurs when a false null hypothesis is
incorrectly accepted (not rejected).
Q26. If we reject the null hypothesis, we might be
making:
A. Type-II error
B. Type-I error ✓ Correct Answer
C. A correct decision always
D. None
Explanation: Rejecting the null hypothesis carries the risk of a
Type-I error, if H₀ was actually true.
Q27. If H₀: New system is no better than the old one,
then the correct decision is:
A. Adopt new system when new one
is better
B. Retain old system when new one
is better
C. Retain old system when
new one is not better ✓ Correct Answer
D. None
Explanation: If H₀ (no improvement) is true, the correct decision is
to retain the old system since the new one is not actually better.
Q28. If H₀: New product is satisfactory, then the
correct statement is:
A. Market new product when
unsatisfactory
B. Market new product when
satisfactory
C. Do not market new product
when unsatisfactory ✓ Correct Answer
D. None
Explanation: If H₀ (satisfactory) is rejected because the product is
actually unsatisfactory, the correct decision is not to market it.
Q29. The significance level, denoted by α, is:
A. The probability of
committing Type-I error ✓ Correct
Answer
B. Power of test
C. The probability of committing
Type-II error
D. None
Explanation: The significance level α is defined as the probability of
committing a Type-I error.
Q30. When the value of α is increased, the
probability of committing a Type-I error is:
A. Decreased
B. Increased ✓ Correct Answer
C. The same
D. None
Explanation: Since α itself is the probability of Type-I error,
increasing α directly increases that probability.
Q31. The value of β gives the:
A. The probability of
committing Type-II error ✓ Correct
Answer
B. Power of test
C. The probability of committing
Type-I error
D. None
Explanation: β represents the probability of committing a Type-II
error (failing to reject a false null hypothesis).
Q32. The value of 1-β gives the:
A. The probability of committing
Type-II error
B. Power of test ✓ Correct Answer
C. The probability of committing
Type-I error
D. None
Explanation: 1-β is the power of the test, i.e. the probability of
correctly rejecting a false null hypothesis.
Q33. Which of the following is not required to apply
the t distribution to make a test of hypothesis about μ?
A. n < 30
B. Population is normally
distributed
C. σ is unknown
D. σ is known ✓ Correct Answer
Explanation: The t-distribution is used precisely when σ is unknown,
so knowing σ is not a requirement for it — in fact it rules out using t.
Q34. The probability of Type-II error is:
A. α
B. 1-β
C. β ✓ Correct Answer
D. 1-α
Explanation: β is, by definition, the probability of committing a
Type-II error.
Q35. The test statistic to test μ₁=μ₂ for a normal
population is:
A. Z-test
B. t-test
C. (a) or (b) ✓ Correct Answer
D. χ²-test
Explanation: Depending on whether the variance is known and the sample
size, either a Z-test or a t-test can be used to compare two means.
Q36. The large sample test for P₁=P₂ for a normal
population is:
A. Z-test ✓ Correct Answer
B. t-test
C. (a) or (b)
D. χ²-test
Explanation: For large samples, the Z-test is used to test equality of
two population proportions.
Q37. For H₁: μ₁ < μ₂, the critical region at α is:
A. Z < -1.6449 ✓ Correct Answer
B. Z > 1.6449
C. Z ≥ 1.6449
D. None
Explanation: A 'less than' alternative hypothesis corresponds to a
left-tailed critical region: Z < -1.6449.
Q38. For H₁: μ₁ > μ₂, the critical region at α is:
A. Z < -1.6449
B. Z > 1.6449 ✓ Correct Answer
C. Z ≤ -1.6449
D. None
Explanation: A 'greater than' alternative hypothesis corresponds to a
right-tailed critical region: Z > 1.6449.
Q39. For H₁: μ₁ ≠ μ₂, the critical region at α is:
A. Z < -1.6449
B. Z > 1.6449
C. Z < -1.6449 or Z >
1.6449 ✓ Correct Answer
D. None
Explanation: A 'not equal to' alternative hypothesis corresponds to a
two-tailed critical region on both sides.
Q40. If one wishes to test the claim that the mean of
the population is 100, the appropriate null hypothesis is:
A. μ = 100 ✓ Correct Answer
B. μ > 100
C. μ ≤ 100
D. μ ≥ 100
Explanation: The null hypothesis always states equality, so testing a
claimed mean value of 100 gives H₀: μ = 100.
Q41. For the Z test, if σ is unknown and n > 30,
we can substitute for σ:
A. n
B. s ✓ Correct Answer
C. t
D. χ²
Explanation: For large samples, the sample standard deviation 's' can
be used in place of the unknown population σ.
Q42. When the t test is used for testing the equality
of two means:
A. Populations must be normal
B. σ₁² = σ₂²
C. n₁, n₂ < 30
D. All ✓ Correct Answer
Explanation: All these conditions — normal populations, equal
variances, and small sample sizes — are required to use the t-test for comparing
two means.
Q43. A statistical hypothesis is an assertion or
conjecture about the:
A. Parameter ✓ Correct Answer
B. Statistic
C. Estimator
D. None
Explanation: A statistical hypothesis is a claim about a population
parameter.
Q44. Hypotheses are usually phrased quantitatively in
terms of:
A. Parameter ✓ Correct Answer
B. Statistic
C. Estimator
D. None
Explanation: Hypotheses are stated numerically in terms of the
underlying population parameter.
Q45. The hypothesis that is tested for possible rejection
is:
A. Null hypothesis ✓ Correct Answer
B. Statistical hypothesis
C. Alternative hypothesis
D. None
Explanation: The null hypothesis is the specific hypothesis that is
directly tested for possible rejection.
Q46. A statement that the investigator attempts to
support with the observed sample is:
A. Null hypothesis
B. Statistical hypothesis
C. Alternative
hypothesis ✓ Correct Answer
D. None
Explanation: The alternative hypothesis represents the claim the
investigator seeks to establish using the sample evidence.
Q47. It completely specifies the underlying
population distribution:
A. Simple hypothesis ✓ Correct Answer
B. Composite hypothesis
C. Statistical hypothesis
D. None
Explanation: A simple hypothesis fully specifies the population
distribution, including all its parameter values.
Q48. It doesn't completely specify the underlying
population distribution:
A. Simple hypothesis
B. Composite hypothesis ✓ Correct Answer
C. Statistical hypothesis
D. None
Explanation: A composite hypothesis leaves some aspect of the
population distribution unspecified.
Q49. The choice of a critical region depends upon:
A. Null hypothesis
B. Alternative
hypothesis ✓ Correct Answer
C. Statistical hypothesis
D. None
Explanation: The direction and shape of the critical region are
determined by the alternative hypothesis.
Q50. Hypothesis never contains the sign of equality:
A. Null hypothesis
B. Alternative
hypothesis ✓ Correct Answer
C. Simple hypothesis
D. None
Explanation: The alternative hypothesis is always stated using <,
>, or ≠ — never an equality sign.
Q51. Hypothesis always contains the sign of equality:
A. Null hypothesis ✓ Correct Answer
B. Alternative hypothesis
C. Composite hypothesis
D. None
Explanation: The null hypothesis is always stated with an equality (=)
sign.
Q52. Set of values of the test statistic for which H₀
is rejected is called:
A. Rejection region
B. Acceptance region
C. Critical region
D. a and c ✓ Correct Answer
Explanation: This set of values is called both the rejection region
and the critical region — the two terms mean the same thing.
Q53. The probability of rejecting a true null
hypothesis is:
A. Level of significance
B. Size of test
C. Confidence level
D. a and b ✓ Correct Answer
Explanation: This probability is known as both the level of
significance and the size of the test.
Q54. The level of significance is the probability of:
A. Rejecting true null hypothesis
B. Type I error
C. Accepting true null hypothesis
D. a and b ✓ Correct Answer
Explanation: The level of significance equals the probability of
rejecting a true null hypothesis, which is exactly the definition of Type I
error.
Q55. The probability of accepting the true null
hypothesis is called:
A. Level of significance
B. Size of test
C. Confidence level ✓ Correct Answer
D. a and b
Explanation: Correctly accepting a true null hypothesis has a
probability equal to the confidence level (1-α).
Q56. A value of the statistic is said to be
statistically significant if it falls in the:
A. Rejection region ✓ Correct Answer
B. Acceptance region
C. Non-rejection region
D. None
Explanation: A statistically significant result is one whose test
statistic falls in the rejection (critical) region.
Q57. Which of these can't be a null hypothesis?
A. θ ≥ θ₀
B. θ ≤ θ₀
C. θ = θ₀
D. θ ≠ θ₀ ✓ Correct Answer
Explanation: A null hypothesis must contain an equality, so θ ≠ θ₀ can
never be a valid null hypothesis.
Q58. Which of these can't be an alternative
hypothesis?
A. θ > θ₀
B. θ < θ₀
C. θ = θ₀ ✓ Correct Answer
D. θ ≠ θ₀
Explanation: Since the alternative hypothesis never contains equality,
θ = θ₀ can never be a valid alternative hypothesis.
Q59. A test statistic is a ratio between the sampling
error and:
A. Bias
B. Standard error ✓ Correct Answer
C. Expectation
D. None
Explanation: A test statistic is generally formed as the ratio of the
sampling (estimation) error to the standard error.
Q60. In a Z-test, degrees of freedom is:
A. n-1
B. n-2
C. n-3
D. None ✓ Correct Answer
Explanation: The Z-test relies on the normal distribution, which
doesn't have a degrees-of-freedom parameter, unlike the t-test.
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