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Tham khảo tài liệu 'statistical concepts in metrology_3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Simpo PDF Merge and Split Unregistered Version - http www.simpopdf.com Date i Xị Observed Corrections to standard 10 gm wt in mg 5-1-63 1 -0.4008 5-1-63 2 0.4053 5-1-63 3 -0.4022 5-2-63 4 -0 4075 5-2-63 5 -0.3994 5-3-63 6 -0.3986 5-6-63 7 -0.4015 5-6-63 8 -0.3992 5-6-63 9 -0 3973 5-7-63 10 -0.4071 5-7-63 11 -0.4012 . . s Xi -4.4201 s X 1.77623417 X -0.40183 mg 1.77611673 n difference 0.00011744 s 2 _Ị1 n 0.00011744 0.000011744 5 0.00343 computed standard deviation of an observed correction about the mean. 0.00103 computed standard deviation of the mean of eleven corrections. computed standard error of the mean. For a two-sided 95 percent confidence interval for the mean of the above sample of size 11 a 2 0.025 V 10 and the corresponding value of t is equal to 2.228 in the table of t distribution. Therefore L X - 0.40183 - 2.228 X 0.00103 -0.40412 V 7Ỉ and L .V r-i -0.40183 2.228 X 0.00103 -0.39954 . V tỉ Data supplied by Robert Ray bold Metrology Division National Bureau of Standards. Comparison Among Two or More Means. The difference between two quantities X and Y to be measured is the quantity mx-v mx my and is estimated by X ỹ where X and ỹ are averages of a number of measurements of X and Y respectively. Suppose we are interested in knowing whether the difference mx_v could be zero. This problem can be solved by a technique previously introduced i.e. the confidence limits can be computed for mx_v and if the upper and lower limits include zero we could conclude that mx-.y may take the value zero otherwise we conclude that the evidence is against mx_y 0. Let us assume that measurements of X and Y are independent with known variances oi and al respectively. By Eq 2.10 2 or for X of n measurements n ƠỈ for ỹ of k measurements k then by 2.8 21 ơ Simpo PDF Merge and Split Unregistered Version - http www.simpopdf.com Therefore the quantity x - j - 0 y n k 2-17 is approximately normally distributed with mean zero and a standard deviation of one under the assumption .