Question
Download Solution PDFGiven below are two statements:
Statement I: If a population from which a sample is to be drawn does not constitute a homogenous group, stratified sampling technique is generally applied in order to obtain a representative sample.
Statement II: In the case of small samples, z-test is applied even if the population standard deviation is not available (given).
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is Statement I is correct but Statement II is incorrect.
Key Points Statement I is correct: If a population from which a sample is to be drawn does not constitute a homogeneous group, stratified sampling technique is generally applied in order to obtain a representative sample. Stratified sampling involves dividing the population into homogeneous subgroups (strata) based on certain characteristics and then drawing samples from each stratum. This helps ensure that the sample represents the diversity within the population.
Statement II is incorrect: In the case of small samples, the t-test is typically applied when the population standard deviation is not available. The t-test is used to test hypotheses about the population mean when the sample size is small and the population standard deviation is unknown. The z-test, on the other hand, is used when the population standard deviation is known or when the sample size is large.
Therefore, the most appropriate answer is that Statement I is correct, but Statement II is incorrect.
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