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Unformatted text preview: Outline for Confidence Intervals and Tests on One Parameter R.L. Andrews (revised April 2006) If the data are from a process then check to assure that the process is stable. Do not attempt statistical inference for an unstable process. Identify the unknown parameter, mean or proportion. If it is a mean, then determine if the standard deviation came from the phenomenon or from the sample. If it is not the sample standard deviation then one must assume that it is the phenomenon standard deviation. If you try to find a standard deviation and cannot find one, then check to see if the unknown parameter is really a proportion rather than a mean. I. Confidence Intervals for location parameters with 100(1 α )% confidence. General form of a 2sided interval for a location parameter: ( Unbiased Estimator ) ± ( M argin of E rror) M argin of E rror [denoted ME ] = (Table Value) • ( S tandard E rror of the estimator [denoted SE ]) The appropriate statistical table and the way the SE value is determined depend on the parameter and information available. The table value can be determined by a statistical table or Excel function{INV}. For 2 tails, α is area in two tails and α /2 is the area in one tail. For 1 tail, α is the area in one tail. For 1sided intervals only subtract or add the appropriate margin of error to get a lower or upper limit. The "t" distribution table with ∞ degrees of freedom is identical to the standard normal distribution A. For an unknown phenomenon MEAN, μ , 1. with the phenomenon variance or standard deviation, σ , known. Use the standard normal distribution. SE = n σ CI: ( 29 x z n ± 1 2 α σ / Z 1 α /2 = NORMSINV(1 α /2) 2. with the phenomenon standard deviation unknown, but estimated with the sample standard deviation, s. Use the "t" distribution with n1 degrees of freedom SE = n s 2sided CI : ( 29 x t s n n ± 1 2 1 α / , t 1 α /2 = TINV( α ,n1) & t 1 α = TINV(2* α ,n1) 1sided lower CI: ( 29 n s t x n 1 , 1 α 1sided upper CI: ( 29 n s t x n + 1 , 1 α B. For an unknown phenomenon PROPORTION , π , with n > 50, n • p>5 & n •(1 p)>5; where p is the sample proportion. Use the standard normal distribution {NORMSINV}....
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 Spring '08
 Andrews,R
 Statistics, Normal Distribution, Standard Deviation, Statistical hypothesis testing, Reject H0

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