Tham khảo tài liệu 'product and process comparisons_4', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Are the data consistent with a nominal standard deviation ENGINEERING STATISTICS HANDBOOK hW tools raids lỉEÂtCH BACK Nixf 7. Product and Process Comparisons . Comparisons based on data from one process . Are the data consistent with a nominal standard deviation The testing of H0 for a single population mean Given a random sample of measurements Y1 . Yn there are three types of questions regarding the true standard deviation of the population that can be addressed with the sample data. They are 1. Does the true standard deviation agree with a nominal value 2. Is the true standard deviation of the population less than or equal to a nominal value 3. Is the true stanard deviation of the population at least as large as a nominal value Corresponding null hypotheses The corresponding null hypotheses that test the true standard deviation Ơ against the nominal value ơg are 1 H0 Ơ cr0 2. Ho ơ a0 3. H0 ơ ơ0 Test statistic The basic test statistic is the chi-square statistic with N -1 degrees of freedom where s is the sample standard deviation . http div898 handbook prc section2 1 of 2 5 1 2006 10 38 33 AM . Are the data consistent with a nominal standard deviation Comparison with critical values For a test at significance level where is chosen to be small typically .01 .05 or .10 the hypothesis associated with each case enumerated above is rejected if 2 _ 2 2 2 1. X Xai2- E orX Xi-ai2 2 2 2. X 2 2 3. X where yW is the upper a 2 critical value from the chi-square distribution with N-1 degrees of freedom and similarly for cases 2 and 3 . Critical values can be found in the chi-square table in Chapter 1. Warning Because the chi-square distribution is a non-negative asymmetrical distribution care must be taken in looking up critical values from tables. For two-sided tests critical values are required for both tails of the distribution. Example A supplier of 100 silicon wafers claims that his fabrication process can produce
