Re: [商管] [統計] 台大統計D

[urml (!#(狗VioL>DoGGiE)]

※ 引述《ONIspirit (嘎)》之銘言：
: 1.
:     _
: Let x be the sample mean of a random sample of size 16 from N(2,4), and
:     _
: let y  be the sample mean of another random sample of size 4 from the
: same parent population
:                           _   _
: Q. Find the probability P(x - y > 0 )
_                _
x ~ N (2, 4/16)  y ~ N(2, 4/4)
_   _
x - y ~ N(0, 4/16 + 4/4) => P(Z>0) = 0.5
: 2.
: An anumal ecologist suggests three methods to prevent squirrels
: from damaging Cryptomeria plantations. To determine the effectiveness
: of the three methods, a small experiment was conducted with 9 replications
: for each treatment(method).
: Mean square error(MSE) of the experiment is 60.
: Please 1) state an appropriate model and its assumptions
:        2) construct a complete ANOVA table based on the given information
:           and state your conclusions. Let the a = 0.05 .
: 　　　　　　　   ────────
:     　　　　　　　   Method
:   　　　　　　　 _______________
:   　
: 　　　　　　     I   II     III
: Treatment Total 243    324   189

1)                          iid
Ⅹij = μ+αi+εij      εij ~ N(0, σ^2)

2)
H0: the effectiveness of the three methods doesn't have sig. diff
vs
H1: the effectiveness of the three methods have sig. diff
df(SST) = 9*3-1 =26
df(SSR) = 2
df(SSE) = 26-2 =24
SSE = 24*60 = 1440
SSR = (243^2+324^2+189^2)/9 - [(243+324+189)^2]/27 =22194 - 21168=1026
SST = SSE + SSR = 2466
        SS      df      MS      F                         Sig
SSR     1026    2       513     8.55>F(.05,2,24) = 3.403  yes
SSE     1440    24      60
SST     2466    26

the effectiveness of the three methods have sig. diff at α=.05

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推 enjoy9003:一開始原PO是不是沒給最下面的那個表!?
→ enjoy9003:我一開始還在想說哪邊可以生出SSR...
→ enjoy9003:我說的是ONI那一篇 這篇解的很正統
→ enjoy9003:另外我想請想問這篇的大大一個解題的技巧@@
→ enjoy9003:當再假設H0H1時 我會習慣於以符號表示 在題目有提出要你
→ enjoy9003:假設的情況下 是不是像你一樣寫會比較好呢?
→ ingles:其實都可以,只要結論下的對就好~
→ urml:@@因為懶所以用複製的~而且題目也沒說他給的數值是啥
→ ingles:原原PO一開始是真的沒給那張表,我也想說那要怎麼算XD
→ urml:假設μ起來還要解釋那是啥的話..可能會不知道要寫啥= =
推 ONIspirit:啊～剛po的時候忘記打上去@@抱歉～非常感謝urml大 :)