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PLOT A VARIABLE WITH NORMAL DISTRIBUTION WITH MEAN 200 AND DEVIATION 20. SUPERIMPOSED WITH THE PREVIOUS FIGURE, PLOT THE DISTRIBUTION OF THE ARITHMETIC MEAN OF SAMPLES OF SIZE N=4, 25 AND 100, OF THAT POPULATION?
shirley mogollon
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.
David Denton
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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 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.
Why is the standard deviation of a distribution of means smaller than the standard deviation of the population from which it was derived?
The reason the standard deviation of a distribution of means is smaller than the standard deviation of the population from which it was derived is actually quite logical. Keep in mind that standard deviation is the square root of variance. Variance is quite simply an expression of the variation among values in the population. Each of the means within the distribution of means is comprised of a sample of values taken randomly from the population. While it is possible for a random sample of multiple values to have come from one extreme or the other of the population distribution, it is unlikely. Generally, each sample will consist of some values on the lower end of the distribution, some from the higher end, and most from near the middle. In most cases, the values (both extremes and middle values) within each sample will balance out and average out to somewhere toward the middle of the population distribution. So the mean of each sample is likely to be close to the mean of the population and unlikely to be extreme in either direction. Because the majority of the means in a distribution of means will fall closer to the population mean than many of the individual values in the population, there is less variation among the distribution of means than among individual values in the population from which it was derived. Because there is less variation, the variance is lower, and thus, the square root of the variance - the standard deviation of the distribution of means - is less than the standard deviation of the population from which it was derived.
When do you know when to use t-distribution opposed to the z-distribution?
z- statistics is applied under two conditions: 1. when the population standard deviation is known. 2. when the sample size is large. In the absence of the parameter sigma when we use its estimate s, the distribution of z remains no longer normal but changes to t distribution. this modification depends on the degrees of freedom available for the estimation of sigma or standard deviation. hope this will help u.... mona upreti.. :)
How many of scores will be within 1 standard deviation of the population mean?
Assuming a normal distribution 68 % of the data samples will be with 1 standard deviation of the mean.
What is standard deviation in concrete technology?
it is in arithmetic
