How to calculate how big of a sample size is needed for the Central Limit Theorem?

Thread starter moonman239
Start date Jul 11, 2011
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Central limit theorem Limit Sample size Theorem

In summary, the Central Limit Theorem is a statistical concept that states that the distribution of sample means will approach a normal distribution when a population is randomly sampled. A sufficiently large sample size is important for this theorem to accurately approximate a normal distribution and estimate the population mean. The necessary sample size can be calculated using the formula n = (z * σ / E)^2, where z is the desired confidence level, σ is the standard deviation of the population, and E is the desired margin of error. The relationship between sample size and confidence level is that larger sample sizes result in higher confidence levels, but also require more resources and time. Other factors, such as population variability and desired precision, should also be considered when determining the sample size for

Jul 11, 2011

moonman239

Is there a way to calculate/estimate how big a sample from a parent distribution would need to be for the distribution of the mean of that sample to be approximately normally distributed?

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Jul 11, 2011

MaxManus

You can't just calculate it, it depends on the distribution of the data. But about 30 is the rule of thumb.

Jul 11, 2011

bpet

The Berry-Esseen theorem may be useful here.

What is the Central Limit Theorem?

The Central Limit Theorem is a statistical concept that states that when a population is randomly sampled, the distribution of sample means will approach a normal distribution regardless of the shape of the original population distribution.

Why is sample size important for the Central Limit Theorem?

The Central Limit Theorem requires a sufficiently large sample size in order to accurately approximate a normal distribution. This ensures that the sample mean will be a good estimate of the population mean.

How do you calculate the necessary sample size for the Central Limit Theorem?

The formula for calculating the sample size needed for the Central Limit Theorem is n = (z * σ / E)^2, where n is the sample size, z is the desired confidence level (e.g. 95% confidence has a z-value of 1.96), σ is the standard deviation of the population, and E is the desired margin of error.

What is the relationship between sample size and confidence level in the Central Limit Theorem?

The larger the sample size, the higher the confidence level will be in accurately approximating a normal distribution. However, larger sample sizes also require more resources and time to collect and analyze.

Are there any other factors to consider when determining sample size for the Central Limit Theorem?

Yes, in addition to the desired confidence level and margin of error, other factors such as the variability of the population and the level of precision needed in the results should also be taken into account when calculating the sample size for the Central Limit Theorem.