Question

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 10,460 16,620 17,400 15,480 12,930 17,260 13,400 13,900 13,630 13,290 14,370 11,700 15,470 17,840 14,030 14,760 4 weeks 9,180 13,250 14,720 12,710 10,120 14,570 11,220 11,100 11,420 10,940 12,110 8,680 12,590 15,090 10,550 12,230 Difference 1280 3370 2680 2770 2810 2690 2180 2800 2210 2350 2260 3020 2880 2750 3480 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 a = 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 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. We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is never the upper bound. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

1 min 4 weeks 10450 91B0 15520 13250 1740） 14720 154B0 12710 12930 10120 17250 14570 13400 11220 13900 11100 13630 11420 13290 10940 14370 12110 11700 253D 15470 12590 17340 15090 14030 10550 14760 total mean dbar- degree of freedom =n-1 std deviaiton sp=/[Zd -(Zaj/n)/(n-1] = std error=se=50/Vn- diff:(d)=x1-x2 1230 1538400.00 3370 11356900.00 2580 7132400.00 2770 7672900.00 2B10 7396100.00 2690 7236100.00 2130 4752400.00 2300 7340000.00 2210 4384100.00 2350 5522500.00 2260 5107600.00 3020 3120400.00 2330 3234400.00 2750 7562500.00 34 30 12110400.00 2530 6 400s00.00 Ed=42050 Ed2=11457B000 2523.750 15.000 517.222 129.3054 12230[

from above

for 95% CI upper bound; and 15 degree of freedom, value of t=			1.753
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		226.679

upper confidence limit                    =

2855.43

O We are 95% confident that the true mean difference between 1-minute modulus and 4-week modulus is at most the upper bound.