As part of a larger project to study the behavior of stressed-skin panels, a str

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.

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.)

If possible, please show work. Thank you.

Observation 1 min 4 weeks Difference 10,490 16,620 17,100 15,480 12,920 17,260 13,400 13,900 13,630 13,230 14,370 11,700 15,470 17,840 14,050 14,760 9,150 13,250 14,720 12,750 10,120 14,570 11,220 11,100 11,420 10,950 12,110 8,650 12,590 15,090 10,550 12,230 1340 3370 2380 2730 2800 2690 2180 2800 2210 2280 2260 3050 2880 2750 3500 2530 2 4 6 7 8 9 10 12 13 14 15 16

Explanation / Answer

here we need to find the upper bound limit for the average difference between the two

the dfference between the two has been given

and we need to find the standard deviation and mean of the data

the alpha = 0.05

therefore the z score = 1.96

the margin of error = 1.96*516.22/sqrt(16) = 252.94

therefore the upper bound = mean + margin of error = 2609.37 + 252.94 = 2862.31

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