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What would happen to the sampling distribution of the mean if you increased the sample size from 5 to 25?
The variance of the estimate for the mean would be reduced.
Advantages and disadvantages of using arithmetic mean?
"The advantage is that the mean takes every value into account. A disadvantage is that it can be affected by extreme values. " The mean or more properly the "arithmetic mean" of a sample will eventually approximate the mean of the distribution of the population as the sample size increases. If the population distribution is skewed (not symmetrical), the mode and median will not provide an estimate of the mean, even as the sample size becomes large.
What does when the sample size and degrees of freedom is sufficiently large the difference between a t distribution and the normal distribution becomes negligible mean?
The t-distribution and the normal distribution are not exactly the same. The t-distribution is approximately normal, but since the sample size is so small, it is not exact. But n increases (sample size), degrees of freedom also increase (remember, df = n - 1) and the distribution of t becomes closer and closer to a normal distribution. Check out this picture for a visual explanation: http://www.uwsp.edu/PSYCH/stat/10/Image87.gif
In statistics if a condition occurs to more than 10 percent of the population is this considered abnormal?
I am under the assumption that in statistics, if the ten percent condition is not met, meaning that the sample size is more than 10% of the population, then the result is not a normal distribution.
Does t-distribution rely on degree of freedom?
Yes. The parameters of the t distribution are mean, variance and the degree of freedom. The degree of freedom is equal to n-1, where n is the sample size. As a rule of thumb, above a sample size of 100, the degrees of freedom will be insignificant and can be ignored, by using the normal distribution. Some textbooks state that above 30, the degrees of freedom can be ignored.
What will be the sampling distribution of the mean for a sample size of one?
It will be the same as the distribution of the random variable itself.
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?
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.
The mean of a binomial probability distribution can be determined by multiplying?
The mean of a binomial probability distribution can be determined by multiplying the sample size times the probability of success.
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.
What affects the standard error of the mean?
The standard error of the underlying distribution, the method of selecting the sample from which the mean is derived, the size of the sample.
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.
What would happen to the sampling distribution of the mean if you increased the sample size from 5 to 25?
The variance of the estimate for the mean would be reduced.
Advantages and disadvantages of using arithmetic mean?
"The advantage is that the mean takes every value into account. A disadvantage is that it can be affected by extreme values. " The mean or more properly the "arithmetic mean" of a sample will eventually approximate the mean of the distribution of the population as the sample size increases. If the population distribution is skewed (not symmetrical), the mode and median will not provide an estimate of the mean, even as the sample size becomes large.
We have a population with mean of 100 and standard deviation of 28 take repeated samples of size 49 and calculate the mean of each sample to form a sampling distribution Is it a Normal Distribution?
a) T or F The sampling distribution will be normal. Explain your answer. b) Find the mean and standard deviation of the sampling distribution. c) We pick one of our samples from the sampling distribution what is the probability that this sample has a mean that is greater than 109 ? Is this a usual or unusual event? these are the rest of the question.
What does when the sample size and degrees of freedom is sufficiently large the difference between a t distribution and the normal distribution becomes negligible mean?
The t-distribution and the normal distribution are not exactly the same. The t-distribution is approximately normal, but since the sample size is so small, it is not exact. But n increases (sample size), degrees of freedom also increase (remember, df = n - 1) and the distribution of t becomes closer and closer to a normal distribution. Check out this picture for a visual explanation: http://www.uwsp.edu/PSYCH/stat/10/Image87.gif
The standard error of the mean is the standard deviation of the sampling distribution of the sample mean?
a large number of samples of size 50 were selected at random from a normal population with mean and variance.The mean and standard error of the sampling distribution of the sample mean were obtain 2500 and 4 respectivly.Find the mean and varince of the population?
How would the mean and standard deviation change if the largest data in each set were removed?
Yes. The standard deviation and mean would be less. How much less would depend on the sample size, the distribution that the sample was taken from (parent distribution) and the parameters of the parent distribution. The affect on the sampling distribution of the mean and standard deviation could easily be identified by Monte Carlo simulation.
