Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 10.1, Problem 5E
Consider the following summary data on the modulus of elasticity (3 106 psi) for lumber of three different grades [in close agreement with values in the article “Bending Strength and Stiffness of Second-Growth Douglas-Fir Dimension Lumber” (Forest Products J., 1991: 35–43), except that the sample sizes there were larger]:
| Grade | J |
|
si |
| 1 | 10 | 1.63 | .27 |
| 2 | 10 | 1.56 | .24 |
| 3 | 10 | 1.42 | .26 |
Use this data and a significance level of .01 to test the null hypothesis of no difference in
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Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean ?1 and standard deviation ?1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean ?2 and standard deviation ?2.
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Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
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Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean μ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean μ2 and standard deviation σ2.
Compute the estimated standard error. (Round your answer to three decimal places.)
(c) Calculate a point estimate of the ratio σ1/σ2 of the two standard deviations. (Round your answer to three decimal places.)
(d) Suppose a single beam and a single cylinder are…
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Chapter 10 Solutions
Probability and Statistics for Engineering and the Sciences
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