Question

WHICH OF THE FOLLOWING FACTORS is not essential for calculating sample size for a single mean estimation
need for statistical significance
assumptions about population standard deviation
precision
significance level

Answer 1

Answer:

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complicated studies there may be several different sample sizes: for example, in a stratified survey, there would be different sizes for each stratum. In a census, data is sought for an entire population, hence the intended sample size is equal to the population. In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group.

Sample sizes may be chosen in several ways:

using experience – small samples, though sometimes unavoidable, can result in wide confidence intervals and risk of errors in statistical hypothesis testing.

using a target variance for an estimate to be derived from the sample eventually obtained, i.e. if high precision is required (narrow confidence interval) this translates to a low target variance of the estimator.

using a target for the power of a statistical test to be applied once the sample is collected.

using a confidence level, i.e. the larger the required confidence level, the larger the sample size (given a constant precision requirement).

Answer 2

Concept

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component. The sample size chosen for a research is typically influenced by the cost, convenience, or ease of data collection as well as the requirement that the sample size have adequate statistical power. Several distinct sample sizes may be used in complex research; for instance, different sample sizes may be used for each strata in a stratified survey. A census gathers information on the whole population,

Explanation

There are numerous options for selecting sample sizes:

• Employing experience - limited samples might result in broad confidence intervals and a danger of mistakes in statistical hypothesis testing, even if they are occasionally inevitable.
• If high accuracy is desired (narrow confidence interval), this corresponds to a low target variance of the estimator. This is done by employing a target variance for an estimate to be produced from the sample that is ultimately acquired.
• Setting a goal for a statistical test's power after the sample has been obtained
• Using a confidence level, the bigger the needed level, the larger the sample size (given a constant precision requirement).

Hence, deviation is not essential for calculating sample size for a single mean estimation.

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