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Height of Women

By calvinw

This is a problem involving the \bar x-distribution and involves finding out how likely a certain size sample mean will be.

Here the idea is to change areas in the \bar x-distribution into areas for the standard normal curve and look them up in the table.

The \mu is the population mean and it corresponds to z=0 as a z-score. The \bar x 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:

z = \frac{{data - mean}}{{stddev}} = \frac{{\bar x- \mu}}{{\frac{\sigma }{{\sqrt n }}}}

Notice that the standard deviation this time on the bottom is

stddev = \frac{\sigma }{{\sqrt n }}

This comes from the Central Limit Theorem and is the form you use when you are working with the \bar x-distribution.

Problem adapted from Larson/Farber’s Elementary Statistics

This entry was posted on May 10, 2007 at 4:15 pm and is filed under Hypothesis Tests - Means, Module 7 Examples. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

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