tailieunhanh - Statistical Concepts in Metrology_2

Tham khảo tài liệu 'statistical concepts in metrology_2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Interpretation and Computation of Simpo PDF Merge and Split Unregistered Version - http By making k sets of n measurements each we can compute and arrange k x s and s s in a tabular form as follows Set Sample mean Sample standard deviation 1 Xj Si 2 x2 S 2 j Xi Sj k xk sk In the array of x s no two will be likely to have exactly the same value. From the Central Limit Theorem it can be deduced that the x s will be approximately normally distributed with standard deviation ơỊ n. The frequency curve of X will be centered about the limiting mean m and will have the scale factor ơịự n. In other words X m will be centered about zero and the quantity _ X m z r ơ n has the properties of a single observation from the standardized normal distribution which has a mean of zero and a standard deviation of one. From tabulated values of the standardized normal distribution it is known that 95 percent of z values will be bounded between and . Hence the statement a v n or its equivalent X 7 m X 1-96 V n fin will be correct 95 percent of the time in the long run. The interval X ơ n to X ơ n is called a confidence interval for m. The probability that the confidence interval will cover the limiting mean in this case is called the confidence level or confidence coefficient. The values of the end points of a confidence interval are called confidence limits. It is to be borne in mind that X will fluctuate from set to set and the interval calculated for a particular Xj may or may not cover m. In the above discussion we have selected a two-sided interval symmetrical about X. For such intervals the confidence coefficient is usually denoted by 1 a where ct 2 is the percent of the area under the frequency curve of z that is cut off from each tail. In most cases Ơ is not known and an estimate of Ơ is computed from the same set of measurements we use to calculate X. Nevertheless let US form a quantity similar to z which is _ X m s n 9 and