统计方法在企业界之应用课件

1、Inference for the Difference in Means-Two Normal Distributions and Variance Unknown&5-3 (&9-3)Why? Horng-Chyi Horng19Statistics II_FiveHorng-Chyi Horng20Statistics II_FiveReplacing s by Sp, we haveHorng-Chyi Horng21Statistics II_FiveHorng-Chyi Horng22Statistics II_FiveExample 9-5 Two catalysts are b

2、eing analyzed to determine how they affect the mean yield of a chemical process. Specially, catalyst 1 is currently in use, but catalyst 2 is acceptable. Since catalyst 2 is cheaper, it should be adopted, providing it does not change the process yield. A test is run in the pilot plant and results in

3、 the data shown in Table 9-2. Is there any difference between the mean yields? Use a = 0.05 and assume equal variances. Horng-Chyi Horng23Statistics II_FiveTable 9-2 Catalyst Yield Data, Example 9-5Horng-Chyi Horng24Statistics II_FiveHorng-Chyi Horng25Statistics II_FiveHorng-Chyi Horng26Statistics I

4、I_Five is distributed approximately as t with degrees of freedom given byHorng-Chyi Horng27Statistics II_FiveHorng-Chyi Horng28Statistics II_FiveHorng-Chyi Horng29Statistics II_FiveHorng-Chyi Horng30Statistics II_FiveC.I. on the Difference in MeansHorng-Chyi Horng31Statistics II_FiveC.I. on the Diff

5、erence in MeansHorng-Chyi Horng32Statistics II_FiveHorng-Chyi Horng33Statistics II_FiveHorng-Chyi Horng34Statistics II_FivePaired t-TestWhen the observations on the two populations of interest are collected in pairs.Let (X11, X21), (X12, X22), , (X1n, X2n) be a set of n paired observations, in which

6、 X1j(m1, s12) and X2j(m2, s22) and Dj = X1j X2j, j = 1, 2, , n. Then, to test H0: m1= m2 is the same as performing a one-sample t-test H0: mD = 0 since mD = E(X1-X2) = E(X1)-E(X2) = m1 - m2 &5-4 (&9-4)Horng-Chyi Horng35Statistics II_FiveHorng-Chyi Horng36Statistics II_FiveExample 9-9 An article in t

7、he Journal of Strain Analysis compares several methods for predicting the shear strength for steel plate girders. Data for two of these methods are shown in Table below. We wish to determine whether there is any difference between the two methods.Horng-Chyi Horng37Statistics II_FiveHorng-Chyi Horng3

8、8Statistics II_FivePaired Vs. UnpairedIf the experimental units are relatively homogeneous (small s) and the correlation within pairs is small, the gain in precision attributable to pairing will be offset by the loss of degrees of freedom, so an independent-sample experiment should be used.If the ex

9、perimental units are relatively heterogeneous (large s) and there is large positive correlation within pairs, the paired experiment should be used. Typically, this case occurs when the experimental units are the same for both treatments; as in Example 9-9, the same girders were used to test the two methods.Horng-Chyi Horng39Statistics II_FiveA Confidence Interval for mDHorng-Chyi Horng40St