Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 14.2, Problem 20E
To determine
Explain whether to use one sample t confidence interval for the true bending rigidity.
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A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4:
323.2
409.5
311.0
326.5
316.8
349.8
309.7
6:
423.1
347.2
361.0
404.5
331.0
348.9
381.7
8:
393.4
366.2
351.0
357.1
409.9
367.3
382.0
10:
362.7
452.9
461.4
433.1
410.6
384.2
362.6
12:
418.4
441.8
419.9
410.7
473.4
441.2
465.8
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: at least two ?i's are equalH0: ?1 = ?2 = ?3 = ?4 = ?5Ha: all five ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 = ?5Ha: at least two ?i's are unequalH0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: all five ?i's are equal
Test the relevant hypotheses using analysis of variance with ? = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Source
Degrees offreedom
Sum…
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
5.5
7.2
7.3
6.3
8.1
6.8
7.0
7.2
6.8
6.5
7.0
6.3
7.9
9.0
8.7
8.7
7.8
9.7
7.4
7.7
9.7
8.0
7.7
11.6
11.3
11.8
10.7
The data below give accompanying strength observations for cylinders.
6.6
5.8
7.8
7.1
7.2
9.2
6.6
8.3
7.0
8.4
7.3
8.1
7.4
8.5
8.9
9.8
9.7
14.1
12.6
11.3
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…
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
5.3
7.2
7.3
6.3
8.1
6.8
7.0
7.1
6.8
6.5
7.0
6.3
7.9
9.0
9.0
8.7
7.8
9.7
7.4
7.7
9.7
7.9
7.7
11.6
11.3
11.8
10.7
The data below give accompanying strength observations for cylinders.
6.8
5.8
7.8
7.1
7.2
9.2
6.6
8.3
7.0
9.0
7.6
8.1
7.4
8.5
8.9
9.8
9.7
14.1
12.6
11.8
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.
(a) Calculate the estimate for the given data. (Round your answer to three decimal places.) (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a).
V(X − Y)
=
V(X) + V(Y)
=…
Chapter 14 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 14.1 - What conclusion would be appropriate for an...Ch. 14.1 - The article Racial Stereotypes in Childrens...Ch. 14.1 - It is hypothesized that when homing pigeons are...Ch. 14.1 - The article Application of Methods for Central...Ch. 14.1 - An information-retrieval system has ten storage...Ch. 14.1 - The article The Gap Between Wine Expert Ratings...Ch. 14.1 - Criminologists have long debated whether there is...Ch. 14.1 - The article Psychiatric and Alcoholic Admissions...Ch. 14.1 - Prob. 9ECh. 14.1 - Prob. 10E
Ch. 14.1 - Prob. 11ECh. 14.2 - Consider a large population of families in which...Ch. 14.2 - A study of sterility in the fruit fly (Hybrid...Ch. 14.2 - Prob. 14ECh. 14.2 - A certain type of flashlight is sold with the four...Ch. 14.2 - Let X = the number of adult police contacts for a...Ch. 14.2 - In a genetics experiment, investigators looked at...Ch. 14.2 - The article A Probabilistic Analysis of Dissolved...Ch. 14.2 - Each headlight on an automobile undergoing an...Ch. 14.2 - Prob. 20ECh. 14.2 - Prob. 21ECh. 14.2 - The article A Method for the Estimation of Alcohol...Ch. 14.2 - The article Nonbloated Burned Clay Aggregate...Ch. 14.3 - The accompanying two-way table was constructed...Ch. 14.3 - In an investigation of alcohol use among college...Ch. 14.3 - Contamination of various food products is an...Ch. 14.3 - The article Human Lateralization from Head to...Ch. 14.3 - Prob. 28ECh. 14.3 - The accompanying data on degree of spirituality...Ch. 14.3 - Three different design configurations are being...Ch. 14.3 - A random sample of smokers was obtained, and each...Ch. 14.3 - Eclosion refers to the emergence of an adult...Ch. 14.3 - Prob. 33ECh. 14.3 - Prob. 34ECh. 14.3 - Prob. 35ECh. 14.3 - Consider the accompanying 2 3 table displaying...Ch. 14 - The article Birth Order and Political Success...Ch. 14 - Does the phase of the moon have any bearing on...Ch. 14 - Prob. 39SECh. 14 - The authors of the article Predicting Professional...Ch. 14 - The accompanying two-way frequency table appears...Ch. 14 - Prob. 42SECh. 14 - Prob. 43SECh. 14 - Prob. 44SECh. 14 - Prob. 45SECh. 14 - The NCAA basketball tournament begins with 64...Ch. 14 - Have you ever wondered whether soccer players...Ch. 14 - Do the successive digits in the decimal expansion...Ch. 14 - Prob. 49SE
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