Statistics

Statistical Sampling Theory – MCQ

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Last Updated on: 17th June 2025, 12:39 pm

Statistical Sampling Theory – MCQ

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1. The opposite of sampling is
(a) Counting
(b) Census
(c) Testing
(d) All of the above.

    The opposite of Sampling is Census. Census means counting as a whole. Sampling means counting as a small portion of a population.
    So, Option (b) is correct.

    2. Method used in testing the human blood is called in statistical terminology
    (a) Census examination
    (b) Blood investigation
    (c) Original investigation
    (d) Sample investigation.

      For testing human blood sample test is conducted because entire human blood can not be tested. So Census examination, original investigation can not be conducted.
      So, Option (d) is correct.

      3. When the population is divided into groups, called
      (a) Block
      (b) Group
      (c) Population
      (d) Cluster.

      When entire population is divided into some recognizable subdivision, it is called cluster in statistical terms.
      So, Option (d) is correct.

        4. A population is perfectly homogeneous in respect of a characteristic. What size of sample would you prefer ?
        (a) A single item
        (b) 5% of population
        (c) 10% of population
        (d) Non item.

        If a population is perfectly homogeneous in respect of a characteristic, then sample consisting of a single item is adequate for statistical analysis.
        So, Option (a) is correct.

        5. As the sample size increases, standard error
        (a) Increases
        (b) Decreases
        (c) Constant
        (d) Decreases proportionately

        If sample size increases, standard deviation of a statistic decreases. So, standard error decreases with increase of sample size.
        So, Option (b) is correct.

        6. The difference between sample S.D. and the estimate of population S.D. is negligible if the sample size is
        (a) Small
        (b) Moderate
        (c) Sufficiently large
        (d) Large.

        The difference between sample S.D and population S.D is negligible if sample size is sufficiently large because sample characteristic will be very near to population characteristic.

        So, Option (c) is correct.

        7. The confidence limits are upper & lower limits of the
        (a) Point estimate
        (b) Interval estimate
        (c) Confidence interval
        (d) None.

        The confidence limits are upper & lower limits of the confidence interval.

        So, Option (c) is correct.

          8. Formula to calculate class limits at 95% confidence level
          (a) \displaystyle \overline{X}\pm 2\sigma
          (b) \displaystyle \overline{X}\pm 1.96\text{ }SE
          (c) \displaystyle \overline{X}\pm 3\text{ }SE
          (d) None.

          The formula \displaystyle X\pm 1.96\text{ }SE is used to calculate class limits at 95% confidence level

          So, Option (b) is correct.

            9. When number of observations are more than 30, the following test of significance is applied
            (a) Z test
            (b) F test
            (c) t test
            (d) None.

            (a) Z test – Correct; used for large samples (e.g, when number of observations are more than 30).

            (b) F test – Used for variance ratio.

            (c) t test – For small samples.

            (d) None – Irrelevant, Not true.

            So, Option (a) is correct.

              10. In Hypothesis Testing when H0 is true, it is called
              (a) Type I error
              (b) Type II error
              (c) Type III error
              (d) Type 0 error.

              Type I error means Rejection of H0 although it is true.
              Type II error means acceptance of H0, although it is False.

              So, Option (a) is correct.

              11. P(type I error) means
              (a) P (accepting H0 when H1 is true)
              (b) P (rejection of H0 when H0 is true)
              (c) P (accepting H0 when H0 is true)
              (d) P (rejection of H0 when H1 is true)

              P(type I error) means P (rejection of H0 when H0 is true)

              So, Option (b) is correct.

              12. When the null hypothesis is H0 : \displaystyle \mu = 42, one sides the alternative hypothesis can be
              (a) \displaystyle {{H}_{1}}:\mu \ge 42
              (b) \displaystyle {{H}_{1}}:\mu <42
              (c) \displaystyle {{H}_{1}}:\mu =42
              (d) \displaystyle {{H}_{1}}:\mu \ne 42 .

              Alternative hypothesis for
              Null hypothesis \displaystyle {{H}_{0}}:\mu =42
              {1}}:\mu \ne 42\{{H}{1}}:\mu >42\text{ or }{{H}_{1}}:\mu <42\end{array}$, for one sided alternative

                So, Option (b) is correct.

                13. Which of the following is a necessary condition for using a f distribution table?
                (a) n is small
                (b) s is known but \displaystyle \sigma is not
                (c) The population is infinite
                (d) (a) and (b) but not (c).

                Necessary condition for using a f distribution table is :
                n is small & s is known but \displaystyle \sigma is not known.

                  So, Option (d) is correct.

                  14. Standard error of mean may be defined as the standard deviation in the sampling distribution of
                  (a) Mean
                  (b) Median
                  (c) Mode
                  (d) None.

                  Standard error of mean may be defined as the standard deviation in the sampling distribution of Mean

                  So, Option (a) is correct.

                  15. A sample survey is subject to
                  (a) Sampling errors
                  (c) (a) or (b)
                  (d) Both (a) and (b).

                  A sample survey is subject to sampling errors, as well as non-sampling errors.
                  (b) Non-sampling errors

                  So, Option (d) is correct.

                  16. The standard error of the_________ is the standard deviation of sample means.
                  (a) Mean
                  (b) Median
                  (c) Mode
                  (d) None.

                  The standard error of the mean is the standard deviation of sample means.

                  So, Option (a) is correct.

                  17. There are_____ types of estimates about a population parameter.
                  (a) One
                  (b) Two
                  (c) Three
                  (d) four

                  There are two type of estimates about a population parameter
                  (1) point estimate
                  (2) interval estimate

                  So, Option (b) is correct.

                  18. We use t-distribution when the sample size is
                  (a) Big
                  (b) Small
                  (c) Moderate
                  (d) None.

                  In case of small sample (usually less than 30), t-distribution is used.

                  So, Option (b) is correct.

                  19. For 3 sample values, we have_________ degree of freedom.
                  (a) 2
                  (b) 3
                  (c) 4
                  (d) 5 .

                  For n sample values, degrees of freedom is n-1.
                  So, For 3 sample values degree of freedom is 2

                  So, Option (a) is correct.