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10 Cards in this Set
- Front
- Back
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t statistics (predicted value of Bj- Bjo)/(standard error of Bj) is normally distributed when...
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Y l X is normal or Y given X is normal
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to choose an appropriate critical value (rejection region) what do we need to know?
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the probability density functions of YlX
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what type of results do we use to approximate the distribution of our test statistic?
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asymptotic results
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does does 'asymptotic' mean?
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it is what happens when N approaches INFINITY
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What are the two theorems that deal with asymptotic results?
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1. Law of Large Numbers
2. Central Limit theorem |
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What is the law of large numbers?
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1 of 2 theorems that deal with asymptotic results where given random sampling, the sample mean approaches (in probability) the population mean E(x)
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How can we get our sample mean to get arbitrarily close to E(x) (population mean)?
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by choosing N sufficiently large (large sample size)
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what happens when 1/x is approaching '0'?
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we are getting close to certainty
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What is the 'central limit theorem'?
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2nd of 2 theorems that deal with asymptotic results where given random sampling, the sample mean is normally distributed with mean E(x) and variance σ^2/N for sufficiently large N
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Under the law of large numbers, what happens to when N increases (or # of observations increases?)
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variance shrink, graphically the variance of scores becomes more and more like a spike (which is called a degenerate). Also the sample mean approaches the population mean.
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