The main advantage of using statistical sampling techniques is that such techniques:

 Options:

a) mathematically measure risk b) eliminate the need for judgmental sampling c) defines the values of tolerable error d) all of the them

The Correct Answer Is:

a) mathematically measure risk

Correct Answer Explanation: a) mathematically measure risk

The main advantage of using statistical sampling techniques is that such techniques mathematically measure risk. This ability to quantify risk is a fundamental aspect of statistical sampling and is crucial for making informed decisions and drawing valid conclusions in various fields, from business and finance to healthcare and quality control.

Statistical sampling techniques involve the systematic selection of a subset, or sample, from a larger population. This sample is chosen in a way that ensures it represents the characteristics of the entire population.

The process is not arbitrary or based on personal judgment, but rather, it relies on mathematical principles and statistical methods to ensure objectivity and accuracy.

The measurement of risk is inherent to statistical sampling techniques in the following ways:

i. Precision and Confidence Intervals:

Statistical sampling allows us to estimate population parameters with a known level of precision. For example, when we take a sample from a population and calculate a parameter like the mean, we can calculate a confidence interval around that estimate.

This interval gives us a range within which the true population parameter is likely to lie, thus quantifying the level of risk associated with our estimate.

ii. Sampling Error:

Statistical sampling acknowledges that there will always be some level of error associated with estimates based on a sample.

By quantifying this sampling error, we gain a clear understanding of how much our sample estimate might deviate from the true population value. This understanding of error is critical for decision-making.

iii. Hypothesis Testing:

Statistical sampling techniques provide tools for hypothesis testing. When we make hypotheses about a population, we can use statistical tests.

To determine whether the evidence from our sample supports or contradicts these hypotheses. This process involves assessing the risk of making a Type I (false positive) or Type II (false negative) error.

iv, Statistical Significance:

In many applications, it is essential to determine whether observed differences or effects are statistically significant.

Statistical significance helps in identifying meaningful patterns or relationships while considering the risk of concluding that a difference exists when it does not (Type I error) or that a difference does not exist when it does (Type II error).

Now, let’s address why the other options are not correct:

b) Eliminate the need for judgmental sampling:

This statement is not entirely accurate. While statistical sampling techniques provide a more structured and objective approach compared to judgmental sampling (where decisions are made based on personal judgment), they do not completely eliminate the need for judgment.

There are still decisions to be made regarding the sampling method, sample size, and other parameters. However, they significantly reduce subjectivity and bias in the sampling process.

c) Define the values of tolerable error:

This is not the primary advantage of statistical sampling techniques. While these techniques do allow us to estimate and quantify error or variability in our sample results, they do not define the specific values of tolerable error.

The determination of tolerable error is typically a subjective decision made based on the context of the study and its requirements.

d) All of the above:

While statistical sampling techniques do involve mathematical measurement of risk, they do not eliminate the need for judgmental sampling, and they do not define specific values of tolerable error. Therefore, the correct answer is not “d) all of the above.”

In summary, the primary advantage of using statistical sampling techniques lies in their ability to mathematically measure risk, providing a structured and systematic way to draw conclusions about a population based on a representative sample.

This ensures that decisions and inferences made from the sample are supported by rigorous statistical principles. The quantification of risk is essential in making informed decisions and reducing the potential for error and bias in various applications.

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