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Ledolter and Hogg (see References) report that two rubber

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 13E Chapter 7.2

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 13E

Ledolter and Hogg (see References) report that two rubber compounds were tested for tensile strength. Rectangular materials were prepared and pulled in a longitudinal direction. A sample of 14 specimens, 7 from compound 𝐴 and 7 from compound 𝐵, was prepared, but it was later found that two 𝐵 specimens were defective and they had to be removed from the test. The tensile strength (in units of 100 pounds per square inch) of the remaining specimens are as follows:

𝐴:         32         30         33         32         29         34         32

𝐵:         33         35        36         37         35

Calculate a 95% confidence interval for the difference of the mean tensile strengths of the two rubber compounds. State your assumptions.

Step-by-Step Solution:

Step 1 of 13

Let X denote the tensile strength of the material from the rubber compound A, and let Y denote the tensile strength of the material from the rubber compound B. It follows from the Central Limit Theorem that is  approximately, and is approximately, where and are the means and are the variances of X and Y, respectively.

Step 2 of 13

Chapter 7.2, Problem 13E is Solved
Step 3 of 13

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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Ledolter and Hogg (see References) report that two rubber