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When the population standard deviation is known the sampling distribution is a?
normal distribution
When the population standard deviation is known the sampling distribution is known as what?
normal distribution
What is the sampling distribution when the standard deviation is known?
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 know the sampling distribution is a?
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.
Why you need sampling distribution?
in order to calculate the mean of the sample's mean and also to calculate the standard deviation of the sample's
When the population standard deviation is not known the sampling distribution is a?
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.
When the population standard deviation is known the sampling distribution is a?
normal distribution
When the population standard deviation is known the sampling distribution is known as what?
normal distribution
What is the sampling distribution when the standard deviation is known?
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.
What is the standard error of the sampling distribution equal to when you do not know the population standard deviation?
You calculate the standard error using the data.
When the population standard deviation is unknown the sampling distribution is equal to what?
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
What is sampling distribution of the mean?
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.
When may the sampling distribution of x̅ be considered to be approximately normal?
the standard deviation of the population(sigma)/square root of sampling mean(n)
Is the standard deviation of the sampling distribution of the sample mean is o?
NO
You take an SRS of size n from a population that has mean 80 and standard deviation 20 How big should n be so that the sampling distribution has standard deviation 1?
400
As the sample size increases the standard deviation of the sampling distribution increases?
No.
What is Confidence Intervals of Standard Error?
The standard deviation associated with a statistic and its sampling distribution.
