Tham khảo tài liệu 'product and process comparisons_5', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Confidence intervals Constrution of exact two-sided confidence intervals based on the binomial distribution If the number of failures is very small or if the sample size N is very small symmetical confidence limits that are approximated using the normal distribution may not be accurate enough for some applications. An exact method based on the binomial distribution is shown next. To construct a two-sided confidence interval at the 100 1 - Q confidence level for the true proportion defective p where Nd defects are found in a sample of size N follow the steps below. 1. Solve the equation CÍ 2 for PU to obtain the upper 100 1 - ữ limit for p. 2. Next solve the equation Note Example of calculation of upper limit for binomial confidence intervals using EXCEL XiK l-Pz l-ce 2 for pl to obtain the lower 100 1 - ữ limit for p. The interval pl pu is an exact 100 1 - q confidence interval for p. However it is not symmetric about the observed proportion defective p N N. The equations above that determine pL and pU can easily be solved using functions built into EXCEL. Take as an example the situation where twenty units are sampled from a continuous production line and four items are found to be defective. The proportion defective is estimated to be p 4 20 . The calculation of a 90 confidence interval for the true proportion defective p is demonstrated using EXCEL spreadsheets. http div898 handbook prc section2 3 of 9 5 1 2006 10 38 37 AM . Confidence intervals Upper confidence limit from EXCEL To solve for pU 1. Open an EXCEL spreadsheet and put the starting value of in the A1 cell. 2. Put BINOMDIST Nd N A1 TRUE in B1 where Nd 4 and N 20. 3. Open the Tools menu and click on GOAL SEEK. The GOAL SEEK box requires 3 entries. li o B1 in the Set Cell box q 2 in the To Value box o A1 in the By Changing Cell box. The picture below shows the steps in the procedure. Final step 4. Click OK in the GOAL SEEK box. The number in A1 .
