1. Chapter Five (&9) Decision Making for Two Samples

2. Horng-Chyi HorngStatistics II_Five2 Chapter Outlines n Inference for a Difference in Means Variance KnownVariance Known Two Normal Distributions, Variance UnknownTwo Normal Distributions, Variance Unknown Paired t-Test Paired t-Test n Inference on the Variances of Two Normal Populations n Inference on Two Population Proportions n Summary Table

3. Horng-Chyi HorngStatistics II_Five3 Introduction

4. Horng-Chyi HorngStatistics II_Five4 Inference for a Difference in Means - Variance Known &5-2 (&9-2)

5. Horng-Chyi HorngStatistics II_Five5 Inference for a Difference in Means - Variance Known

6. Horng-Chyi HorngStatistics II_Five6 Hypothesis Tests for a Difference in Means - Variance Known

7. Horng-Chyi HorngStatistics II_Five7 Example 9-1 A product developer is interested in reducing the drying time of a primer paint. Two formulations of the paint are tested; formulation 1 is the standard chemistry, and formulation 2 has a new drying ingredient that should reduce the drying time. From experience, it is known that the standard deviation of drying time is 8 minutes, and this inherent variability should be unaffected by the addition of the new ingredient. Ten specimens are painted with formulation 1,and another l0 specimens are painted with formulation 2; the 20 specimens are painted in random order. The two sample average drying times are 121 min. and 112 min., for formulation 1 and 2 respectively. What conclusions can the product developer draw about the effectiveness of the new ingredient, using α=0.05?

8. Horng-Chyi HorngStatistics II_Five8

9. Horng-Chyi HorngStatistics II_Five9 The Sample Size (I) Assume that H 0 :  1 -  2 =  0 is false and the true difference is  Given values of  and , find the required sample size n to achieve a particular level of . Given values of  and , find the required sample size n to achieve a particular level of .

10. Horng-Chyi HorngStatistics II_Five10 The Sample Size (II) n Two-sided and one-sided Hypothesis Testings

11. Horng-Chyi HorngStatistics II_Five11 Example 9-2

12. Horng-Chyi HorngStatistics II_Five12 Example 9-3

13. Horng-Chyi HorngStatistics II_Five13 Identifying the Cause and Effect n In Example 9-1 n Factors, Treatments, and Response Variables n Completely Randomized Experiments Randomly assigned 10 test specimens to one formulation, and 10 test specimens to the other formulation.Randomly assigned 10 test specimens to one formulation, and 10 test specimens to the other formulation. n Observational Study Not randomizedNot randomized Maybe caused by other factors not considered in the studyMaybe caused by other factors not considered in the study ExamplesExamples

14. Horng-Chyi HorngStatistics II_Five14 Confidence Interval on a Difference in Means - Variance Known

15. Horng-Chyi HorngStatistics II_Five15 Example 9-4 n Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. The test data is listed in Table 5-1. Find a 90% C.I. on the difference of the tensile strength of these two aluminum spars.

16. Horng-Chyi HorngStatistics II_Five16

17. Horng-Chyi HorngStatistics II_Five17 Choice of Sample Size to Achieve Precision of Estimation Where E is the error allowed in estimating  1 -  2.

18. Horng-Chyi HorngStatistics II_Five18 One-Sided C.I.s on the Difference in Means – Variance Unknown A 100(1-  ) percent upper-confidence interval on  1 -  2 is A 100(1-  ) percent upper-confidence interval on  1 -  2 is And a 100(1-  ) percent lower-confidence interval is And a 100(1-  ) percent lower-confidence interval is