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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             10,450 9,130   1320 2             16,620 13,250   3370 3             17,500 14,720   2780 4             15,480 12,710   2770 5             12,960 10,120   2840 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             13,210 10,940   2270 11             14,370 12,110   2260 12             11,700 8,640   3060 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 𝛼 = 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 at least 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 exactly the upper bound.

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