Question 81

Given below are two statements :
Statement I : The statistical constant of the population are known as parameters.
Statement II : The square root of the standard deviation of the sampling
distribution of a statistic is known as the standard error.
In the light of the above statements, choose the most appropriate answer from
the options given below:

Solution

Statement I: "The statistical constants of the population are known as parameters."

This statement is correct. In statistics, parameters are numerical characteristics of a population. They include measures such as the population mean, population variance, population standard deviation, etc. These parameters are fixed values that describe the entire population.

Statement II: "The square root of the standard deviation of the sampling distribution of a statistic is known as the standard error."

This statement is also correct. In statistics, the standard error (SE) measures the variability or precision of a statistic due to random sampling. It is calculated as the standard deviation of the sampling distribution of a statistic. Specifically, the standard error of the sample mean (often denoted as SE or SEM) is the standard deviation of the sampling distribution of the sample means. It represents the average amount that a sample mean deviates from the true population mean. The standard error is indeed calculated by taking the square root of the variance (or standard deviation) of the sampling distribution.

So, both statements are correct. (Option A)


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