2-18-09 - of freedom , is formed. • Based upon...

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Economic Statistics – Class Notes – 2/18/09 Exam #1 Page numbers for this material – in the textbook Recognize the formula for the estimator – t-distribution: Z, t, f, and chi-square distributions We were able to take a form that we did NOT recognize before and transform it into a form that we now CAN recognize (see PROOF above).
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4. The student “t-distribution” – A distribution formed by dividing a standard normal random variable by the square root of a Chi-square random variable that has been divided by its degrees of freedom. “t” distribution comes after Chi-square since the t-distribution is a function of Chi- Square
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I can use sample information to estimate the unknown population mean and variance. * Use this formula: 5. The “F” Distribution – The distribution that results when the ratio of two INDEPENDENT Chi-squared random variables, each of which has been divided by its degrees
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Unformatted text preview: of freedom , is formed. • Based upon Chi-Square, and thus, Z, and thus the Normal Distribution • The normal distribution is the mother of all important distributions that we form. DISTRIBUTIONS: Normal (regular normal) Z t-distribution Chi-Square F-Distribution APPLIED STATISTICS BEGINS… III. Interval Estimators A. Confidence Interval – A formula for determining a range of values that will contain the true population parameter with fixed probability in repeated sampling. Example – A 90% confidence interval for the population mean uses the point estimator (sample mean of X) to find the values for “a” and “b” such that: 1.) The probability in repeated sampling that the confidence interval will not contain (whatever it is we are estimating, like µ ) is a. Alpha is the probability of an error (later, alpha = the level of significance) NO EXERCISE FOR FRIDAY...
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This note was uploaded on 06/03/2009 for the course ECON 203 taught by Professor Casler during the Spring '09 term at Allegheny.

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2-18-09 - of freedom , is formed. • Based upon...

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