統計的仮説検定とExcelによるt検定

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1 I L14( Fri) : Time-stamp: Fri 14:03 JST hig 1,,,, p, Excel p, t. ( ) L14 Excel t I(015) 1 / 0

2 L13-Q1 Quiz : n = 9. σ 0.95, S n 1 (n 1) <σ < S χ α <σ < <σ < 64. χ 1 α n 1 (n 1) L13-Q Quiz : n = 9., X = 1 9 [ ] = 80g., S = [(78 80) + + (8 80) ] = 4g., µ 80g, σ 4g. ( ) L14 Excel t I(015) / 0

3 µ 0.95, S X t 0.05 (9 1) n <µ < X + t 0.05(9 1) <µ < <µ < σ 0.95, S n 1 (n 1) <σ < S χ α <σ < <σ < χ 1 α n 1 (n 1) S n ( ) L14 Excel t I(015) 3 / 0

4 3 4 Excel t Excel ( ) L14 Excel t I(015) 4 / 0

5 ( ) N(µ, σ ), σ 0!(σ 0 ) H 1 σ σ 0. ( ) H 0 σ = σ 0. n S,, Y = (n 1) S, n 1. σ0 y 0 = χ 1 α (n 1), y 1 = χ α (n 1) ( ) L14 Excel t I(015) 5 / 0

6 1 α = 0.95, ( ) P χ 1 α (n 1) < (n 1) S σ0 < χ α (n 1) = 1 α., S,, S S < σ 0 χ 1 α (n 1), σ0 n 1,. χ α (n 1) < S n 1 ( ) L14 Excel t I(015) 6 / 0

7 L14-Q1 TA Prob and Sol: S, σ 0 = 4g., S 9, ( g). 76, 76, 76, 76, 80, 84, 84, 84, 84. S σ, σ 0?, α = 0.05,. 1 α = 0.05,. ( ) L14 Excel t I(015) 7 / 0

8 3, σ, σ0 = 4 4 n S, χ = (n 1) s, n 1. σ0. 5 χ = (n 1) s = (9 1) 16 σ0 4 = 3. 6,, χ < χ 1 α (n 1) =.180, χ > χ α (n 1) = σ 0 = 4.,. σ0 ( σ0 )., p Excel p, p = < α,. ( ) L14 Excel t I(015) 8 / 0

9 3 4 Excel t Excel ( ) L14 Excel t I(015) 9 / 0

10 ,, q 0 = H 1 q q 0 H 0 q = q 0 : 100 X. X = 0, 5, 6,..., 100. ( ) L14 Excel t I(015) 10 / 0

11 L14-Q q 0 = 0.03,, α. α., α. ( ) L14 Excel t I(015) 11 / 0

12 L14-Q3 q( q 0 ),, β., 1 β β.. ( ) L14 Excel t I(015) 1 / 0

13 ,, H 0 H 0 H 0 ( β ) H 0 1 ( α ) α: 1 α: 1 β: or, β α., α, β. ( ) L14 Excel t I(015) 13 / 0

14 p (t ) p (p-value),. p < α. ( ) L14 Excel t I(015) 14 / 0

15 Excel 3 4 Excel t Excel ( ) L14 Excel t I(015) 15 / 0

16 Excel Excel 013 Excel average var stdev : average, varp, stdevp. ( ) L14 Excel t I(015) 16 / 0

17 Excel Excel 013 t n: t Excel p =t.dist.rt(t, n) t =t.inv( p, n) Excel Excel,. R II, II ( ) L14 Excel t I(015) 17 / 0

18 Excel Excel t T T p p < α t, t II ( ) L14 Excel t I(015) 18 / 0

19 Excel Excel 013 n: t Excel p =chisq.dist.rt(y 1, n) 1 p =chisq.dist.rt(y 0, n) y 1 =chisq.inv( p, n) y 0 =chisq.inv(1 p, n) ( ) L14 Excel t I(015) 19 / 0

20 Excel t Math., Quiz , Quiz 4 6(1-50) manaba / ryukoku.ac.jp ( ) L14 Excel t I(015) 0 / 0

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