Which of the following statements is correct?
|a) Lower the sampling risk greater the sample size|
b) Smaller the tolerable error, greater the sample size
c) Lower the expected error, smaller the sample size
d) All are correct
The Correct Answer Is:
d) All are correct
The correct answer is indeed option “d) All are correct.”
Let’s delve into the details to understand why this answer is correct and why the other options are not:
a) Lower the sampling risk, greater the sample size:
This statement is correct. Sampling risk refers to the risk that the sample you select may not accurately represent the entire population. By increasing the sample size, you can reduce this risk.
A larger sample size provides more data points and is more likely to reflect the true characteristics of the population, which helps in minimizing sampling errors and risk.
b) Smaller the tolerable error, greater the sample size:
This statement is also correct. Tolerable error, also known as margin of error, is the maximum acceptable difference between the sample estimate and the true population parameter. If you want a smaller margin of error, you’ll need a larger sample size.
This is because a larger sample size provides more data points and, as a result, allows for more precise estimation, reducing the margin of error.
c) Lower the expected error, smaller the sample size:
This statement is correct as well. The expected error, in the context of statistical sampling, is the anticipated difference between the sample estimate and the true population parameter. If you aim for a lower expected error, you can achieve it with a smaller sample size if the population is homogenous and variability is low.
In cases where the population is not very diverse, a smaller sample can provide accurate estimates. However, in cases with high variability or diverse populations, a larger sample size is needed to reduce expected error.
Now, let’s explain why the other options are not correct: