Test: Sampling Theory - 2 - SSC CGL MCQ

The text describes the Law of Statistical Regularity as a key principle, which states that if a large sample size is drawn from the population under discussion at random, then on an average the sample will provide characteristics of that population.

According to the Principle of Inertia, large numbers are likely to be more reliable, accurate, and precise as the sample size increases, provided other factors are kept constant.

The Principle of Optimization ensures that an optimum level of efficiency at a minimum cost or the maximum efficiency at a given level of cost can be achieved with the selection of an appropriate sampling design.

The text explains that increasing the sample size would put an extra burden on available resources, time, and efficiency, hence it's not always possible or feasible.

The text defines 'population' as the aggregate of all the units under consideration, also referred to as the 'universe'.

Sampling errors are defined as the deviation between the value of population parameter as obtained from a sample and its observed value.

The text lists errors due to defective sampling design as a sampling error, not a non-sampling error.

The population mean, denoted by μ in the formula, represents the average length of life of all the lamps produced by General Electricals in the example given.

The text suggests that complete enumeration is preferred when detailed information is necessary, the population size is not large, or when the occurrence of a particular attribute is so rare that it might merit complete enumeration.

The text points out that sample surveys can usually be conducted much more quickly than complete enumeration or censuses, making speed a primary advantage.

The total number of possible samples without replacement is given by the combination formula
C(n,k), which for n = 5 and k = 3 is 10.

With replacement, each of the three elements can be paired with any of the three, including itself, for a total of
3²=9
3² =9 samples.

The table provided shows an equal probability for the sample means obtained, indicating a uniform distribution.

The sampling distribution table shows the mean of the sample means to be 3.

Given that, Number of observations = 5

Hence, the mean of 5 observations is:

Mean = (38 + 51 + 46 + 79 + 57)/5 = 54.2

Now, the standard deviation is calculated as follows:

Standard Deviation, SD = √[(Σ(x_i – x̄)²) / (N-1)]

Now, substitute the values in the formula, we get

On solving the above expression, we get

S.D = 15.5

Hence, the standard deviation (S.D) of their heights is 15.5.

The population, or universe, in the context of sampling, refers to all the units under consideration for the survey.

In SRS, each unit has an equal chance of being selected, which is based on a fixed probability.

Stratified sampling is used to divide a heterogeneous population into smaller, more homogeneous groups to ensure that the sample accurately represents the population.

Systematic sampling is known for being less time-consuming and simpler compared to other methods of sampling.

Judgement sampling relies on the discretion of the sampler to select units based on their knowledge or opinion, not on probability.

If there is an unknown and undetected periodicity in the sampling frame, systematic sampling can introduce a bias linked to that periodicity.

Purposive or Judgement Sampling is non-probabilistic because it relies on the subjective judgment of the sampler rather than random selection.

Multi-stage sampling allows for more manageable sampling from a large and heterogeneous population by breaking down the process into several stages.

'k' systematic sampling is a type of linear systematic sampling where the first unit is selected randomly and subsequent units are selected at regular intervals of k.

Purposive sampling is based on the judgment of the sampler and is non-probabilistic, which means that it does not allow for statistical inferences to be made about the population parameters.

Bowley's allocation suggests that sample sizes for different strata are taken as proportional to the population sizes when the strata variances differ significantly among themselves, we take recourse to “Neyman’s allocation.”

Multi-stage sampling involves several stages of sampling, each nested within the other, until the ultimate sampling unit is reached and selected as an example.

Multi-stage sampling is known to be cost-effective because it simplifies the process, especially in large and complex populations, but this can sometimes come at the cost of lower accuracy compared to more direct sampling methods.

Circular systematic sampling is used when the population size N is not a multiple of the sample size n, allowing for the sampling procedure to continue in a circular manner until the required sample size is obtained.

If N is not a multiple of n, circular systematic sampling is used, which involves continuing the count from the top after reaching the bottom of the list.