10-31-07 - Large Sample Confidence Interval for the Mean =...

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Unformatted text preview: Large Sample Confidence Interval for the Mean = 55g Weight of Diaper n = 30 _ x = 54.98 Must fix interval of confidence. 90% or 95% We are 95% confident that value will be found in interval. Example: we would like to be able to say that based on the sample data, the interval from 54.50 55.50g covers with a probability of 95%. Confidence interval has lower boundary (L) and upper boundary (U). Confidence interval has probability level called the confidence level: (1x) In our example: x = 5% So... 1x = 95% (We construct a confidence interval of 100) A confidence interval for a population is in general in the following form: P(L < < U) = 1 x The value of z needed to construct a confidence interval is called a critical value. n = 30 _ X = 54.98 = 55 1 x = 95% 5% 0.025 Z = 1.96 L = 54.98 1.96 = 54.78 U = 54.98 + 1.96 = 55.18 Unknown: If n is large enough we can use s to estimate for . Formula becomes: Degrees of Freedom If n = 30 observations, we have n 1 degrees of freedom. If n is small and is unknown, then the sampling distribution of x is called a t distribution. ...
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This note was uploaded on 04/18/2008 for the course ECON 205 taught by Professor Diagne during the Fall '07 term at Towson.

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10-31-07 - Large Sample Confidence Interval for the Mean =...

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