FREE IGNOU MCO-03 SOLVED ASSIGNMENT 2023

d) Large samples and Small samples

Large Samples: A large sample refers to a substantial subset of the population, typically involving a large number of observations. In statistical terms, a large sample size is generally considered to be greater than 30. Large samples have several characteristics:

1. Representativeness: Large samples tend to be more representative of the population as they encompass a wide range of observations.
2. Precision: With a large sample, the estimates tend to be more precise and closer to the true population parameters.
3. Statistical Power: Large samples have higher statistical power, making it easier to detect significant relationships or differences in the data.
4. Reduced Sampling Error: The sampling error (the difference between the sample statistic and the population parameter) is reduced in large samples.
5. More Reliable Inferences: Inferences based on large samples are more reliable and have greater external validity.

Small Samples: A small sample refers to a subset of the population that includes a limited number of observations. In statistical terms, a small sample size is typically considered to be less than 30. Small samples have some characteristics:

1. Limited Representativeness: Small samples may not fully represent the diversity and variability present in the population, leading to potential bias.
2. Higher Sampling Error: The sampling error is relatively higher in small samples, leading to less precise estimates.
3. Lower Statistical Power: Small samples have lower statistical power, making it harder to detect significant relationships or differences.
4. Less Reliable Inferences: Inferences based on small samples are less reliable and may have limited external validity.
5. Resource Constraints: Small samples are often chosen due to practical limitations, such as time, cost, or accessibility.

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