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Unformatted text preview: Introduction, 1 sample t-test and t-interval Central Limit Theorem Let X 1 ,X 2 ,...,X n be a random sample from a distribution with mean and variance 2 .Then if n is sufficiently large (Rule of thumb > 30), X has approximately a normal distribution with X = and 2 X = 2 /n t distribution When X is the mean of a random sample of size n from a normal distribution with mean , the random variable t = X- s/ n has a probability distribution called t distribution with n-1 degrees of free- dom. Experiment example 87 individuals were given a flu vaccination. After 28 days, blood samples were taken to assess the concentration of antibody ( X ) in their serum. Some summary statistics for the sample are as follows. n = 87, X = 1 . 689, s = 1 . 549. Assume that the sample is from a normal population with mean and vari- ance 2 . 1 Confidence interval for the mean of a normal population The form of the 100(1- ) % confidence interval for is x t / 2 ,n- 1 s n where t / 2 ,n- 1 is the upper / 2 percentage point of the t distribution with n- 1 degrees of freedom. To find a 99% CI, = . 01, so / 2 = . 005 n = 87, so there are 86 degrees of freedom t . 005 , 86 t . 005 , 75 = 2 . 643 (using 75 degrees of freedom, which is the df nearest 86 from t table...
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This note was uploaded on 03/27/2012 for the course ECON 2280 taught by Professor Daniel during the Spring '12 term at Dalhousie.
- Spring '12