【正文】 enter in Hypothesized p. (The alternative proportion is not the value of the alternative hypothesis, but the value at which you want to evaluate power.) Page 81 2 proportion ? For a twosample test of proportion, enter the expected proportions under the null hypothesis for Proportion 2 in the dialog box. ?Suppose a biologist wants to test for a difference in the proportion of fish affected by pollution in two lakes. The biologist would like to detect a difference of and suspects that about one quarter () of fish in Lake A have been affected. ?假設(shè)： H0: p1 = p2 H1: p1 ≠ p2 ?In Minitab, enter and in Proportion 1 values。ll have a 71% chance of detecting a difference if you send out 1000 surveys to each. If the population proportions are actually and , you39。 Page 76 Power and Sample Size 1Sample t計量型數(shù)據(jù) ?Suppose you are the production manager at a dairy plant. In order to meet state requirements, you must maintain strict control over the packaging of ice cream. The volume cannot vary more than 3 oz for a halfgallon (64oz) container. The packaging machine tolerances are set so the process ? is 1. How many samples must be taken to estimate the mean package volume at a confidence level of 99% (a = .01) for power values of , , and ?（需要樣本量大??？） ?Minitab操作： 1 Choose Stat Power and Sample Size 1Sample t. 2 In Differences, enter 3. In Power values, enter . 3 In Standard deviation, enter 1. 4 Click Options. In Significance level, enter . Click OK in each dialog box Page 77 Interpreting the results 結(jié)果分析 ?分析結(jié)果 ： Power and Sample Size 1Sample t Test Testing mean = null (versus not = null) Calculating power for mean = null + difference Alpha = Assumed standard deviation = 1 Sample Target Difference Size Power Actual Power 3 5 3 5 3 6 ? Interpreting the results（結(jié)果說明）： Minitab displays the sample size required to obtain the requested power values. Because the target power values would result in noninteger sample sizes, Minitab displays the power (Actual Power) that you would have to detect differences in volume greater than three ounces using the nearest integer value for sample size. If you take a sample of five cartons, power for your test is 。 Page 74 Factors that influence power影響功效的因素 ? a the probability of a Type I error (level of significance). As the probability of a Type I error ( a) increases, the probability of a type II error (?) decreases. Hence, as a increases, power = 1 also increases. ? 當 a風(fēng)險（生產(chǎn)方風(fēng)險） ↑, ? 風(fēng)險（消費方風(fēng)險） ↓，power=1 ? ↑ ? σ, the variability in the population. As s increases, power decreases. ? 當總體 σ ↑， power ↓ ? the size of the population difference (effect). As the size of population difference effect) decreases, power decreases. ? 總體差異△ ↓， power ↓ ? sample size. As sample size increases, power increases. ? 樣本大?。?n） ↑ ， power ↑。即第二類錯誤的可能性 P= ?。也叫 拒真 風(fēng)險或是生產(chǎn)方風(fēng)險。 Page 72 a風(fēng)險與 ? 風(fēng)險 Our Decision （得出結(jié)論） Null Hypothesis（真實狀況） H0=True H0=False Fail to reject H0不能拒絕 H0 Correct Decision 1a Type Ⅱ error 取偽錯誤 ? 風(fēng)險 Reject H0 拒絕 H0 Type Ⅰ error 拒真錯誤 a風(fēng)險 Correct Decision 1? Power=1 ? Page 73 a風(fēng)險與 ? 風(fēng)險 ? When H0 is true and you reject it, you make a Type I error. The probability (p) of making a Type I error is called alpha (a ) and is sometimes referred to as the level of significance for the test. ?當 H0原假設(shè)是正確的而你拒絕它，你將犯第一類錯誤。功效就是當 H0原假設(shè)是錯誤時正確的拒絕它的可能性。LSL→Pr Z bench： 定義？ P→Z 中心極限定理 : 定義 ? 關(guān)注點 ? Y=f(X): 變量分類 ? 改進重點邏輯 ? 提高過程能力的重點 ? 過程改進的焦點 ? 知 識 關(guān) 口 Page 71 功效與樣本大?。?Power and Sample Size） What is Power? ? There are four possible outes for a hypothesis test. The outes depend on whether the null hypothesis (H0) is true or false and whether you decide to reject or fail to reject H0. The power of a test is the probability of correctly rejecting H0 when it is false. In other words, power is the likelihood that you will identify a significant difference (effect) when one exists. ? 一種假設(shè)檢定有四種可能結(jié)果。來源？分類？ 計量數(shù)據(jù) amp。 正態(tài)分布 Page 67 提高過程能力 因變量 Y（響應(yīng)變量），取決于自變量 X（獨立變量） 至關(guān)重要的少數(shù)變量也被稱為 “杠桿”變量 ，因為它們對因變量具有重大影響。 正態(tài)分布 Page 64 Z值與 DPMO計算 MINITAB： Calc﹥ Probability Distributions﹥ N