What should be my sample size?
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What should be the sample size?
The sample size can be determined using the following equation:
where;
- n = the number of samples (it’s always rounded up)
- zα/2 = is the value of the z-statistic for the given confidence level (α).
- σ = analogous to the standard deviation of the sample.
- SE = Sampling error or margin or error.
For the zα/2:
zα/2 90 % confidence interval 1.645 95 % confidence interval 1.96 99 % confidence interval 2.575
For σ: It is either known from a previous study or estimated as Range / 4.
Example:
According to a Food and Drug Administration (FDA) study, a cup of coffee contains an average of 115 milligrams (mg) of caffeine, with the amount per cup ranging from 60 to 180 mg. Suppose we want to repeat the FDA experiment to obtain an estimate of the true mean caffeine content in a cup of coffee to within 5 mg with 90% confidence. How many cups of coffee would have to be included in the sample?
- σ ≈ R / 4 = 180 − 60 / 4 = 30 mg
- zα/2 = 1.645
- SE = 5
- Using the equation we get:
- n = (1.645) 2 (30) 2 / (5)2 = 97.4 rounded up to 98.
98 cups of coffee would be a sufficient sample size for this study.
Keep in mind that if you are performing a survey, it is n, not the % that matters. What we mean by this is that if I take a random sample of 100 students in a college, this represents the student body just as well as a random sample of 100 voters represents the ENTIRE electorage of the United States. This is surprising. If you have 1000 respondents (n = 1000), this will ALWAYS give you a margin of error of plus or minus 3 percentage points with 90% confidence. And it doesn't matter if the population size is 100,000 or 30 million.
For SURVEYS, it is the n, not the % that matters.
If there are any questions or concerns, please feel free to have a chat with your math teacher. Most highschools cover statistics to some degree, and teachers should be able to clarify any issues.
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