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A normal distribution with a mean of 200 and a deviation of 20 can be plotted as a bell-shaped curve, as shown in the figure below.
Superimposed on the figure, the distribution of the arithmetic mean of samples of size n=4, 25 and 100 can be plotted as shown in the figure below. The arithmetic mean distribution for n=4 is a much narrower distribution than a normal distribution, since it is based on a small sample size. As the sample size increases, the distribution becomes wider and more similar to the normal distribution.
What else can I help you with?
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.
The standard deviation of the distribution of means is also known as the population standard deviation?
Yes.
When to use z or t-distribution?
If the sample size is large (>30) or the population standard deviation is known, we use the z-distribution.If the sample sie is small and the population standard deviation is unknown, we use the t-distribution
The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown?
It can be.
What is standard deviation of the mean?
If repeated samples are taken from a population, then they will not have the same mean each time. The mean itself will have some distribution. This will have the same mean as the population mean and the standard deviation of this statistic is the standard deviation of the mean.
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
The standard deviation of the distribution of means is also known as the population standard deviation?
Yes.
When the population standard deviation is known the sampling distribution is known as what?
normal distribution
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.
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 to use z or t-distribution?
If the sample size is large (>30) or the population standard deviation is known, we use the z-distribution.If the sample sie is small and the population standard deviation is unknown, we use the t-distribution
The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown?
It can be.
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 standard deviation of the mean?
If repeated samples are taken from a population, then they will not have the same mean each time. The mean itself will have some distribution. This will have the same mean as the population mean and the standard deviation of this statistic is the standard deviation of the mean.
What is a t distribution?
The t distribution is a probability distribution that is symmetric and bell-shaped, similar to the normal distribution, but has heavier tails. It is used in statistics, particularly for small sample sizes, to estimate population parameters when the population standard deviation is unknown. The t distribution accounts for the additional uncertainty introduced by estimating the standard deviation from the sample. As the sample size increases, the t distribution approaches the normal distribution.
When the population standard deviation is known the sample distribution is a?
When the population standard deviation is known, the sample distribution is a normal distribution if the sample size is sufficiently large, typically due to the Central Limit Theorem. If the sample size is small and the population from which the sample is drawn is normally distributed, the sample distribution will also be normal. In such cases, statistical inference can be performed using z-scores.
