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- University
- Politecnico di Milano
- Degree programme
- Energy Engineering
- Subject
- Statistica per L'ingegneria
- Academic year
- 2015-2016
- Classification
- Exam · Second midterm
- Content
- Exam paper only
- Original format
- Text
- Searchable text
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ExamSecond midtermExam paper only
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Study material for Statistica per L'ingegneria, shared by the Studwiz community and reviewed by moderators.
Statistica per L'ingegneriaSecond midterm
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X 2 = 29 µ µ X x100 = 16.1557,s 2 100 = 27.78307, Histogram of x x Frequency 5 1015202530 0 5 10 15 20 ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ●● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ● ● ● ● ●● ●● ●●● ● ● ● ● ● ● ● ● ● ● ●● ● −2−10 1 2 5 10 15 20 25 30 Normal Q−Q Plot Theoretical Quantiles Sample Quantiles SW−pvalue = 1.589e−06 µ H0 H1 n 2 z2 0.005 = 29 · 2.5762 = 192.4 () n 193 x100 ± p 100 z0.005 = 16.16 ± 1.39 (14.77 , 17.55) n = 100 H0 : µ = 15,H 1 : µ 6= 15,R : x100 15 > p 100 z0.005 () 15 /2 x100 ± p 100 z0.005 15 2 16.16 ± 1.39 H0 NO x ¯x = 179.5 s2 = 24.8 2 ¯x = 176.5 s2 = 39.6 2 ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● −2 −1 0 1 2 175180185 NPP SENSORE VECCHIO Theoretical Quantiles Sample Quantiles ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● −2 −1 0 1 2 170175180185 NPP SENSORE NUOVO Theoretical Quantiles Sample Quantiles H0 H1 NO x • X • X H0 : 2 = 2 ,H 1 : 2 6= 2 ,R ↵ : ⇢ s2 s2 <f 1 ↵ 2 (21, 19) [ ⇢ s2 s2 >f ↵ 2 (21, 19) X ⇠ N (µ , 2 ),X ⇠ N (µ , 2 ). s2 s2 =0 .63 < 1 s2 s2 =0 .63 = f1 ↵ 2 (21, 19) = 1 f ↵ 2 (19, 21) 0.56 = 1 1.78 = 1 f0.1(20, 21) ' 1 f0.1(19, 21) < 0.63 = 1 f ↵ 2 (19, 21) < 1 f0.25(19, 21) ' 1 f0.25(20, 21) = 1 1.35 =0 .74 0.2 <↵ = < 0.5 NO x X X H0 : µ µ ,H 1 : µ >µ ,R ↵ : t0 >t 0.05(40), t0 = ¯x ¯x sP p 1/22 + 1/20 s2 P = 21 s2 + 19 s2 40 . X ⇠ N (µ , 2),X ⇠ N (µ , 2), t0 = ¯x ¯x sP p 1/22 + 1/20 =1 .72 >t 0.05(40) = 1 .684, H0 Y T D Y 101520 ● ●● ●● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ●●● ●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●…
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