Chapter Five (&9)

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

2. Chapter Outlines • Inference for a Difference in Means • Variance Known • Two Normal Distributions, Variance Unknown • Paired t-Test • Inference on the Variances of Two Normal Populations • Inference on Two Population Proportions • Summary Table Statistics II_Five

3. Introduction Statistics II_Five

4. Inference for a Difference in Means-Variance Known &5-2 (&9-2) Statistics II_Five

5. Inference for a Difference in Means-Variance Known Statistics II_Five

6. Hypothesis Tests for a Difference in Means-Variance Known Statistics II_Five

7. 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? Statistics II_Five

8. Statistics II_Five

9. The Sample Size (I)Assume that H0: m1-m2 = 0 is false and the true difference is • Given values of a and , find the required sample size n to achieve a particular level of b. Statistics II_Five

10. The Sample Size (II) • Two-sided and one-sided Hypothesis Testings Statistics II_Five

11. Example 9-2 Statistics II_Five

12. Example 9-3 Statistics II_Five

13. Identifying the Cause and Effect • In Example 9-1 • Factors, Treatments, and Response Variables • Completely Randomized Experiments • Randomly assigned 10 test specimens to one formulation, and 10 test specimens to the other formulation. • Observational Study • Not randomized • Maybe caused by other factors not considered in the study • Examples Statistics II_Five

14. Confidence Interval on a Difference in Means- Variance Known Statistics II_Five

15. Example 9-4 • 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. Statistics II_Five

16. Statistics II_Five

17. Choice of Sample Size to Achieve Precision of Estimation Where E is the error allowed in estimating m1-m2. Statistics II_Five

18. One-Sided C.I.s on the Difference in Means – Variance Unknown • A 100(1-a) percent upper-confidence interval on m1-m2 is • And a 100(1-a) percent lower-confidence interval is Statistics II_Five