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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 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.
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.
How many observations to assume a Normal distribution?
32 if you sample is a random sample. Other methods look at the shape of the data and how skewed it is.
Is the standard deviation of the sampling distribution of the sample mean is o?
NO
