The mean of the distribution of sample means X is equal to t

The mean of the distribution of sample means X is equal to the mean of the population from which the samples are drawn. If we draw a sample of 3i2e 40 from a large population, the distribution of X will be approximately normal. For a given sample size, the width cf 90% confidence interval for mu will be shorter than for 80% confidence interval. If X has a normal distribution with a near, of 25 and a standard deviation of 2, then 50% of the data values of X are less than 25. For a sample of size 36 from a large population, with mu = 65 and sigma = 15, the standard deviation of the distribution of the sample mean X is 2.5. The mean A in a sample study provides a point estimate of the population mean mu. The standard deviation of the sample mean X decreases as the sample size n increases. The distribution of the sample mean X is approximately normal when the sample size n is large. As the degrees of freedom become large, the t-distribution approaches the Z-distribution. One of the assumptions for using a t-distribution is that the sample be drawn from a normal population.

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