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1、Hypothesis Testing & Sample Size Selection,2,Scope of Module,HypothesisSampling RisksOne-Tailed and Two-Tailed TestsP-ValueApplications of Hypothesis TestingImportance of sample size for hypothesis testingDrift Sensitivity-Risk and -RiskSample Size Determination,3,Hypothesis,A hypothesis is a statem
2、ent or claim about a property of a population.The hypothesis to be tested consists of two complementary statements:1)The null hypothesis (denoted by H0) is a statement about the value of a population parameter; it must contain the condition of equality. 2)The alternative hypothesis (denoted by H1) i
3、s the statement that must be true if the null hypothesis is false.e.g.H0: = some valuevs H1: some valueH0: some valuevs H1: some valueH0: some valuevs H1: 0 H1: .05 = Normal,17,Testing for 2 populations,H0: variance of process 1 = variance of process 2F-TestH0: mean of process 1 = mean of process 22
4、-Sample t-Test (equal variances)2-Sample t-Test (unequal variances)H0: proportion of process 1 = proportion of process 22-Proportions TestH0: the 2 populations are correlatedCoefficient of Correlation(to be discussed in Correlation module),18,F Test (H0: 1 = 2),Compares the sample variance from two
5、populations.Accept H0 if , reject H0 if otherwise.,19,Example,A study was performed to evaluate the effectiveness of improving LPC (Liquid Particle Count) of U6 actuator. A time after ECD & cleaning is a KPIV to study. 10 pcs samples were record from each groups (10 mins & 20 mins).Determine if the
6、variance in LPC is similar for two different time. The LPC data is stored in C2 & C3 on “3. Hypothesis Testing. MTW”,20,Example,Stat Basic Statistics 2 Variances,21,Example,Test for Equal VariancesLevel1 10 minsLevel2 20 minsConfLvl 95.0000 Bonferroni confidence intervals for standard deviations Lower Sigma Upper N Factor Levels 975.48 1491.29 3002.93 10 10 mins 1782.06 2724.35 5485.90 10 20 mins F-Test (normal distribution) Test Statistic: 0.300P-Value : 0.087,22,Example,23,2-Sample t-Test Unequal (H0: 12 = ),
