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# Notes 12 - Notes 12 Recall The sample mean x is the best...

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Notes 12 Recall : The sample mean x is the best estimate of the population mean μ . This is an example of a point estimate. Point Estimate : a single-value estimate of the population parameter. Instead of being restricted to a single value for an estimate, a range of values can be used as an estimate. This is called an Interval Estimate . Interval Estimate : an interval that is estimated to contain the value of a population parameter. Example : The sample mean height for American men is 69". (Point Estimate) Instead, we can say that the mean height of American men is between 67.5" and 70.5" (Interval Estimate). How do you determine the size of this interval? How do you determine the upper and lower boundaries for this interval? These questions are answered using COglyph1197FIDEglyph1197CE Iglyph1197TERVALS . The Idea Behind the Confidence Interval Recall that 95% of the z-scores fall within 2 standard deviations of the mean. We can rewrite the previous statement as it is equivalent to saying the probability that z lies between -2 and 2 is approximately equal to .95. or P( -2 < z < 2 ) =0.95 Recall this graph and assume we have a standard normal distribution with μ =0 and σ=1.

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Notes 12 Therefore, our level of confidence is just simply the probability of a population parameter being contained in a confidence interval for a point estimate of a sample. Example: So using the same example from the previous page: The mean height of American men is between 67.5 and 70.5 inches with a level of confidence of C =.95 can be read as the following: Whenever a sample of American men is drawn and a confidence interval is constructed from the sample data, 95% of the samples (of American men) will yield an interval that actually contains the mean height of all men.
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Notes 12 - Notes 12 Recall The sample mean x is the best...

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