Anonymous
Anonymous asked in 科學數學 · 9 years ago

信賴區間之問題.

隨機抽出九輛裝設省油裝置的汽車,並記錄其裝設前後行駛100公里的耗油量

(單位1加侖)

車號 裝設前 裝設後

1 3.2 2.9

2 4.6 4.7

3 3.6 3.2

4 5.3 5.0

5 6.2 5.7

6 3.2 3.3

7 3.6 3.4

8 4.5 4.3

9 3.9 3.5

假設每輛汽車耗油量呈常態分配.求汽車裝設前與裝設後行駛100公里的平均耗油量差的95%信賴區間.

1 Answer

Rating
  • 匿名
    Lv 6
    9 years ago
    Favorite Answer

    因為裝設前後是對應同一輛車, 所以要先計算出裝設前-裝設後的數據

    假設X為裝設前-裝設後的耗油量

    X_bar = (0.3+(-0.1)+0.4+0.3+0.5+(-0.1)+0.2+0.2+0.4)/9 = 0.2333

    sd^2 = (0.3^2+(-0.1)^2+0.4^2+0.3^2+0.5^2+(-0.1)^2+0.2^2+0.2^2+0.4^2-9*(0.2333)^2)/(9-1) = 0.045

    sd = sqrt(0.045) = 0.2121

    X_bar~Normal(μ=0.2333, sd=0.2121)

    汽車裝設前與裝設後行駛100公里的平均耗油量差的95%信賴區間:

    = X_bar +/- t(0.025,8)*sd

    = 0.2333 +/- 2.306*0.2121

    = 0.2333 +/- 0.4892

    = [-0.2558, 0.7225]

    2011-11-24 04:36:20 補充:

    95%信賴區間:

    = X_bar +/- t(0.025,8)*sd/sqrt(9)

    = 0.2333 +/- 2.306*0.0707

    = 0.2333 +/- 0.1631

    = [0.0703, 0.3964]

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