s part of a larger project to study the behavior of stressed-skin panels, a structural component being used extensively in North America, an article reported on various mechanical properties of Scotch pine lumber specimens. Data on the modulus of elasticity (MPa) obtained 1 minute after loading in a certain configuration and 4 weeks after loading for the same lumber specimens is presented here. Observation 1 min 4 weeks Difference 1 10,460 9,190 1270 2 16,620 13,250 3370 3 17,300 14,720 2580 4 15,480 12,730 2750 5 12,930 10,120 2810 6 17,260 14,570 2690 7 13,400 11,220 2180 8 13,900 11,100 2800 9 13,630 11,420 2210 10 13,260 10,940 2320 11 14,370 12,110 2260 12 11,700 8,690 3010 13 15,470 12,590 2880 14 17,840 15,090 2750 15 14,060 10,550 3510 16 14,760 12,230 2530 Calculate an upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus; first check the plausibility of any necessary assumptions. (Use ? = 0.05. Round your answer to two decimal places.) MPa Interpret your upper confidence bound. We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is never the upper bound.We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is exactly the upper bound. We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is at most the upper bound.We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is at least the upper bound.

s part of a larger project to study the behavior of stressed-skin panels, a structural component being used extensively in North America, an article reported on various mechanical properties of Scotch pine lumber specimens. Data on the modulus of elasticity (MPa) obtained 1 minute after loading in a certain configuration and 4 weeks after loading for the same lumber specimens is presented here. Observation 1 min 4 weeks Difference 1 10,460 9,190 1270 2 16,620 13,250 3370 3 17,300 14,720 2580 4 15,480 12,730 2750 5 12,930 10,120 2810 6 17,260 14,570 2690 7 13,400 11,220 2180 8 13,900 11,100 2800 9 13,630 11,420 2210 10 13,260 10,940 2320 11 14,370 12,110 2260 12 11,700 8,690 3010 13 15,470 12,590 2880 14 17,840 15,090 2750 15 14,060 10,550 3510 16 14,760 12,230 2530 Calculate an upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus; first check the plausibility of any necessary assumptions. (Use ? = 0.05. Round your answer to two decimal places.) MPa Interpret your upper confidence bound. We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is never the upper bound.We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is exactly the upper bound. We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is at most the upper bound.We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is at least the upper bound.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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As part of a larger project to study the behavior of stressed-skin panels, a structural component being used extensively in North America, an article reported on various mechanical properties of Scotch pine lumber specimens. Data on the modulus of elasticity (MPa) obtained 1 minute after loading in a certain configuration and 4 weeks after loading for the same lumber specimens is presented here.

Observation	1 min	4 weeks	Difference
1	10,460	9,190	1270
2	16,620	13,250	3370
3	17,300	14,720	2580
4	15,480	12,730	2750
5	12,930	10,120	2810
6	17,260	14,570	2690
7	13,400	11,220	2180
8	13,900	11,100	2800
9	13,630	11,420	2210
10	13,260	10,940	2320
11	14,370	12,110	2260
12	11,700	8,690	3010
13	15,470	12,590	2880
14	17,840	15,090	2750
15	14,060	10,550	3510
16	14,760	12,230	2530

Calculate an upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus; first check the plausibility of any necessary assumptions. (Use ? = 0.05. Round your answer to two decimal places.)
MPa

Interpret your upper confidence bound.

We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is never the upper bound.We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is exactly the upper bound. We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is at most the upper bound.We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is at least the upper bound.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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