Chapter_23_notes (1) - Chapter 23 Inference about Means So far we have seen how to find probabilities concerning the sample mean we use the Central

# Chapter_23_notes (1) - Chapter 23 Inference about Means So...

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Chapter 23: Inference about Means So far we have seen how to find probabilities concerning the sample mean: we use the Central Limit Theoremunder certain conditions: 1. The sample size is large. 2. The population from which the sample is taken is not heavily nonnormal. 3. The population standard deviation, , is known. (This one is the kicker. It is almost impossible for us to know what this true value is.)
When is not known we must come up with other statistical tools to estimate or test the population mean. Typically, we have been substituting the sample standard deviation sfor the standard deviation of x, sn, for . When the standard deviation of a statistic, like x, is estimated from the data, the result is called the standard errorof the statistic. ex. SEsnxRecall, that our basis for inference so far has revolved around zxnwhere znormal(0,1) if is known.
If is not known then txsnhas a different distribution known as a t-distribution.