The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
the standard deviation of the population(sigma)/square root of sampling mean(n)
400
64.
From what ive gathered standard error is how relative to the population some data is, such as how relative an answer is to men or to women. The lower the standard error the more meaningful to the population the data is. Standard deviation is how different sets of data vary between each other, sort of like the mean. * * * * * Not true! Standard deviation is a property of the whole population or distribution. Standard error applies to a sample taken from the population and is an estimate for the standard deviation.
the standard error will be 1
If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.
normal distribution
normal distribution
When the standard deviation of a population is known, the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, due to the Central Limit Theorem. The mean of this sampling distribution will be equal to the population mean, while the standard deviation (known as the standard error) will be the population standard deviation divided by the square root of the sample size. This allows for the construction of confidence intervals and hypothesis testing using z-scores.
When the population standard deviation is not known, the sampling distribution of the sample mean is typically modeled using the t-distribution instead of the normal distribution. This is because the t-distribution accounts for the additional uncertainty introduced by estimating the population standard deviation from the sample. As the sample size increases, the t-distribution approaches the normal distribution, making it more appropriate for larger samples.
You calculate the standard error using the data.
Thanks to the Central Limit Theorem, the sampling distribution of the mean is Gaussian (normal) whose mean is the population mean and whose standard deviation is the sample standard error.
the standard deviation of the population(sigma)/square root of sampling mean(n)
NO
400
No.
The standard deviation associated with a statistic and its sampling distribution.