Class 4 - Outline Conf. Interval Hyp. Test

# Class 4 - Outline Conf. Interval Hyp. Test - Outline for...

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Outline for Confidence Intervals and Tests on One Parameter R.L. Andrews (revised 10/20/2010) If the data are from a process first check to assure that the process is stable. Do not attempt statistical inference for an unstable process. Identify the unknown parameter, proportion or mean. 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 parameter may be a proportion rather than a mean. I. Confidence Intervals for location parameters with 100(1- α )% confidence. General form of a 2-sided interval for a location parameter: ( Unbiased Estimator ) ± ( M argin of E rror) ( Sample based Estimate ) ± ( M argin of E rror) M argin of E rror [denoted ME ] = (Table Value) ( S tandard E rror of the estimator [denoted SE ]) ( Sample based Estimate ) ± (Table Value)•( S tandard E rror) 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 (A-42&43 or A-44) or Excel function (NORMSINV, NORMINV or TINV). For the standard normal, the text table A-42&43 and Excel functions use cumulative probability, hence Z 1- α denotes a table value with 1- α area below it and α in the upper tail and Z 1- α /2 and 1- α/2 area below and α/2 in the upper tail. For the t distribution, the text table E.2 and the Excel functions use tail probabilities, hence t α denotes a table value with α in the upper tail. t α /2 for 2 tail procedures has α = area in two tails and α /2 = the area in one tail. For 1 tail procedures, α is the area in one tail. For 1-sided intervals only subtract or add the appropriate margin of error to get the appropriate lower or upper limit. The "t" distribution table with degrees of freedom is identical to the standard normal distribution A. C.I. for an unknown phenomenon PROPORTION , p, with n p ˆ >10 & n •(1- p ˆ )>10; where p ˆ is the sample proportion. For table values use the standard normal distribution.

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## This note was uploaded on 06/20/2011 for the course MGMT 524 taught by Professor Andrews,r during the Spring '08 term at VCU.

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Class 4 - Outline Conf. Interval Hyp. Test - Outline for...

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