This is a problem involving the 
-distribution and involves finding out how likely a certain size sample mean will be.
Here the idea is to change areas in the -distribution into areas for the standard normal curve and look them up in the table.
The 
is the population mean and it corresponds to z=0 as a z-score. The is a sample mean and it corresponds to a data value in the left graph above. You change it into a z-value in the right graph by using the formula for the z-score:
Notice that the standard deviation this time on the bottom is
This comes from the Central Limit Theorem and is the form you use when you are working with the -distribution.
Problem adapted from Larson/Farber’s Elementary Statistics
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This entry was posted on November 29, 2011 at 6:02 am and is filed under Hypothesis Tests - Means, Module 7 Examples, Sample Means. You can follow any responses to this entry through the RSS 2.0 feed.
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