Tham khảo tài liệu 'engineering statistics handbook episode 9 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Are the data consistent with the assumed process mean and the sample standard deviation is 1 1 _ 2 i-J-M K-K P-M J with N -1 degrees of freedom. Comparison with critical values For a test at significance level o. where is chosen to be small typically .01 .05 or .10 the hypothesis associated with each case enumerated above is rejected if 1. f . L a 2 jV-i 2. t. J 3. t c t. where taỊ2- is the upper cd2 critical value from the t distribution with N-1 degrees of freedom and similarly for cases 2 and 3 . Critical values can be found in the t-table in Chapter 1. Test statistic where the standard deviation is known If the standard deviation is known the form of the test statistic is ƠỈ Vn For case 1 the test statistic is compared with Z JO which is the upper t-Ll 2 critical value from the standard normal distribution and similarly for cases 2 and 3 . Caution If the standard deviation is assumed known for the purpose of this test this assumption should be checked by a test of hypothesis for the standard deviation. An illustrative example of the t-test The following numbers are particle contamination counts for a sample of 10 semiconductor silicon wafers 50 48 44 56 61 52 53 55 67 51 The mean counts and the standard deviation counts. http div898 handbook prc section2 2 of 3 5 1 2006 10 38 31 AM . Are the data consistent with the assumed process mean The test is Over a long run the process average for wafer particle counts has been two-sided 50 counts per wafer and on the basis of the sample we want to test whether a change has occurred. The null hypothesis that the process mean is 50 counts is tested against the alternative hypothesis that the process mean is not equal to 50 counts. The purpose of the two-sided alternative is to rule out a possible process change in either direction. Critical For a significance level of fl .05 the chances of erroneously rejecting values the null hypothesis when it is true are 5 or less.
