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When the sample size is large valid confidence intervals can be established for the population mean irrespective of the shape of the underlying distribution?
Yes, but that begs the question: how large should the sample size be?
What is The mean of a discrete probability distribution is also called the?
The mean of a discrete probability distribution is also called the Expected Value.
A sample of 24 observations is taken from a population that has 150 elements The sampling distribution of the mean is?
A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of is
The mean or expected value of the distribution of a discrete random variable is?
30.47
What does a negative kurtosis mean?
It means distribution is flater then [than] a normal distribution and if kurtosis is positive[,] then it means that distribution is sharper then [than] a normal distribution. Normal (bell shape) distribution has zero kurtosis.
What is the shape of the distribution of the mean of a sample?
The mean of a sample is a single value and so its distribution is a single value with probability 1.
Which of the following is true regarding the sampling distribution of the mean for a large sample size?
It has the same shape, mean, and standard deviation as the population.
How does the number of repetitions effect the shape of the normal distribution?
When we discuss a sample drawn from a population, the larger the sample, or the large the number of repetitions of the event, the more certain we are of the mean value. So, when the normal distribution is considered the sampling distribution of the mean, then more repetitions lead to smaller values of the variance of the distribution.
How much error is expected between the sample mean and population mean?
0. The expected value of the sample mean is the population mean, so the expected value of the difference is 0.
When the sample size is large valid confidence intervals can be established for the population mean irrespective of the shape of the underlying distribution?
Yes, but that begs the question: how large should the sample size be?
What is the mean of the sampling distribution of the sample mean?
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
How do you calculate distribution of sample means?
The sample mean is distributed with the same mean as the popualtion mean. If the popolation variance is s2 then the sample mean has a variance is s2/n. As n increases, the distribution of the sample mean gets closer to a Gaussian - ie Normal - distribution. This is the basis of the Central Limit Theorem which is important for hypothesis testing.
What is the mean of a normal distribution?
It is the expected value of the distribution. It also happens to be the mode and median.It is the expected value of the distribution. It also happens to be the mode and median.It is the expected value of the distribution. It also happens to be the mode and median.It is the expected value of the distribution. It also happens to be the mode and median.
The distribution of sample means consists of?
A set of probabilities over the sampling distribution of the mean.
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 using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
What is the difference between population and sample distribution?
Sampling distribution is the probability distribution of a given sample statistic. For example, the sample mean. We could take many samples of size k and look at the mean of each of those. The means would form a distribution and that distribution has a mean, a variance and standard deviation. Now the population only has one mean, so we can't do this. Population distribution can refer to how some quality of the population is distributed among the population.
