Factors that determine sample size
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1. population to deal with in the sample 2. Location. ocation where the sample will be done 3. design. how the sample will be taken 4. result. how the outcome will be determined
You have not defined M, but I will consider it is a statistic of the sample. For an random sample, the expected value of a statistic, will be a closer approximation to the parameter value of the population as the sample size increases. In more mathematical language, the measures of dispersion (standard deviation or variance) from the calculated statistic are expected to decrease as the sample size increases.
The bigger the sample size the more accurate the results will be. For example, if you roll a 6 sided die and track the results to get the probability of rolling a six. If you only roll 6 times, then you may not even get one 6 or you could get a few. A small sample size means you won't get very reliable results.
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.For Confidence level c, and the critical value of Zc is the number such that the area under the statndard normal curve between -Zc and Zc equals C.n > (zcσ/E)2
When something is a sample size, that means it is smaller than the size that is normally available for purchase. Sample size products are usually enough to let you try something before you buy it.