Which of the following factors are responsible for the E-size of the sample in sampling schemes ?
(i) Precision of the estimates required is an important factor in determining the size of a sample
(ii) For greater precision, usually a larger sample is preferred
(iii) For greater precision usually a smaller sample is preferred
(iv) More is the heterogeneity, a larger is the size of the sample.
MH SET - 2025, SET Exam - 2025,
Answer: B
The correct statements are (i), (ii) and (iv).
The size of a sample depends mainly on the precision required and on how variable the population is. (i) is true: the precision needed in the estimates is a key factor. (ii) is true: the standard error of a mean falls as \(\sigma/\sqrt{n}\), so greater precision needs a larger sample. (iv) is true: the more heterogeneous the population, the larger its variance, and the larger the sample needed for the same precision.
(iii) is false, since it says the opposite of (ii): a smaller sample gives a larger standard error and therefore less precision. Every option containing (iii) is therefore wrong.
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