# 28 - Condition for inference about a mean: We can regard...

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Condition for inference about a mean: We can regard our data as a simple random sample (SRS) from the population. This condition is very important. Observations from the population have a Normal distribution with mean µ and standard deviation σ. In practice, it is enough that the distribution be symmetric and single-peaked unless the sample is very small. Both μ and σ are unknown parameters. : the standard error of the sample mean When the standard deviation of a statistic is estimated from data, the result is called the standard error of the statistic. The standard error of the sample mean is . This z statistic has the standard Normal distribution N(0,1). In practice, we don’t know σ, so we substitute the standard error of for its standard deviation . The statistic that results does not have a Normal distribution. It has a distribution that is new to us, called a t distribution. Draw an SRS of size n from a large population that has the Normal distribution with mean µ and

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## This note was uploaded on 02/27/2012 for the course STAT 121 taught by Professor Patticolling during the Winter '11 term at BYU.

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28 - Condition for inference about a mean: We can regard...

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