On Feb. 8, this year, at 6am in the morning all UiB meteorology professors met to discuss a highly unfortunate and top-urgent crisis: Their most precious instrument, responsible for measuring the air temperature hour-by- hour, had failed - what if the Bergen public would find out? How would they plan their weekend without up-to-date air temperature readings? Silent devastation - and maybe a hint of panic, also - hung in the room. Apprentice Taylor, who - as always - was late to the meeting, sensed that this was his chance to shine! Could they fake the data? At least for some hours (until the measurements would work again)? He used to spend a lot of time online and thus knew the value of fake data, especially when it spread fast! He reminded the crying professors of a prehistoric project with the title "Love your derivatives as you love yourself!" - back then, they had installed top-modern technology that not only measured the air temperature itself, but also its 1st, 2nd, 3rd, 4th, and even its 5th derivatives! Nobody had ever used this research, but today was different. Proudly, Taylor claimed that he could ensure air temperatures would come out "as usual" for at least several hours! Under quite some dust, he quickly found the 6am readings on a fragile looking tape: T\6am T' T" 6am 16am 6am T!!! T!!!! 2.8 19 -100 100/3 640 T!!!!! 6am 6am -675 On the label of the tape, he could also read: "time unit: 1 day (24h)", "uncertainty: ±10%", and "careful with those higher orders!" With all his love for the KISS principle, Taylor decided to first try the lower orders. He quickly constructed models fa(t) of increasing degree d = {0, 1, 2, . . ., 5} for t≥ 0 (with t = 0 corresponding to Feb. 8, 6am, and t = 1 corresponding to Feb. 9, 6am) that would give him fake air temperatures for the coming hours. Write out these model functions for him (up to order 5). Then, he decided to evaluate these models for t € 24. {0, 3, 6, 9, 12, 15, 18, 21, 24}, corresponding to the coming 24 hours (in steps of 3h). Make a 6×9 table with the resulting numbers. If you prefer rounded decimals, round to at least one digit after the comma. Look critically at your table and think: which entries seem trustworthy, which maybe not so much? Discuss your observations. Extra point (not required for "ticking" this exercise as solved): How could the uncertainty-info on the tape label be used to study, until which time on Feb. 8 (or even Feb. 9) the different models are trustworthy?

On Feb. 8, this year, at 6am in the morning all UiB meteorology professors met to discuss a highly unfortunate and top-urgent crisis: Their most precious instrument, responsible for measuring the air temperature hour-by- hour, had failed - what if the Bergen public would find out? How would they plan their weekend without up-to-date air temperature readings? Silent devastation - and maybe a hint of panic, also - hung in the room. Apprentice Taylor, who - as always - was late to the meeting, sensed that this was his chance to shine! Could they fake the data? At least for some hours (until the measurements would work again)? He used to spend a lot of time online and thus knew the value of fake data, especially when it spread fast! He reminded the crying professors of a prehistoric project with the title "Love your derivatives as you love yourself!" - back then, they had installed top-modern technology that not only measured the air temperature itself, but also its 1st, 2nd, 3rd, 4th, and even its 5th derivatives! Nobody had ever used this research, but today was different. Proudly, Taylor claimed that he could ensure air temperatures would come out "as usual" for at least several hours! Under quite some dust, he quickly found the 6am readings on a fragile looking tape: T\6am T' T" 6am 16am 6am T!!! T!!!! 2.8 19 -100 100/3 640 T!!!!! 6am 6am -675 On the label of the tape, he could also read: "time unit: 1 day (24h)", "uncertainty: ±10%", and "careful with those higher orders!" With all his love for the KISS principle, Taylor decided to first try the lower orders. He quickly constructed models fa(t) of increasing degree d = {0, 1, 2, . . ., 5} for t≥ 0 (with t = 0 corresponding to Feb. 8, 6am, and t = 1 corresponding to Feb. 9, 6am) that would give him fake air temperatures for the coming hours. Write out these model functions for him (up to order 5). Then, he decided to evaluate these models for t € 24. {0, 3, 6, 9, 12, 15, 18, 21, 24}, corresponding to the coming 24 hours (in steps of 3h). Make a 6×9 table with the resulting numbers. If you prefer rounded decimals, round to at least one digit after the comma. Look critically at your table and think: which entries seem trustworthy, which maybe not so much? Discuss your observations. Extra point (not required for "ticking" this exercise as solved): How could the uncertainty-info on the tape label be used to study, until which time on Feb. 8 (or even Feb. 9) the different models are trustworthy?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 33PPS

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