發問時間: 社會與文化語言 · 5 年前

統計小題目

Chocolate balls have 7 colors which are brown, yellow, red,orange, green, blue and

black. The company declares that each color has the portion of 30% 、20% 、

15%、15% 、10%、5% and 5%。If a bag of chocolate(500balls) is

selected the color and quantity are following: brown 160, yellow 120, red 80,orange 60, green 45, blue 20, black 15. Use  = 0.01 to determine the declaration of the

company is correct or not.

1.Degree of freedom is .

2.Standard value of χ2 is .

3.Your calculation of χ2 is .

4.Do you accept the declaration of the company?

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解題附上詳解,不要只有答案,謝謝

1 個解答

評分
  • 5 年前
    最佳解答

    嗯,不必擔心,都是很直接的題。

    degree of freedom = 組別 - 1 = 7 - 1 = 6

    (嚴格來說是 (r - 1) × (c - 1) = (2 - 1) × (7 - 1))

    2015-05-31 02:21:09 補充:

    對於 α = 0.05,

    Standard value of χ² 就是

    χ²(α = 0.05, df = 6) = 12.59

    查表得知。

    2015-05-31 02:24:00 補充:

    對於 500 balls, 30% 、20% 、15%、15% 、10%、5% and 5% 分別是

    150, 100, 75, 75, 50, 25, 25 個球

    這些是 Ei

    而 Oi 分別是 160, 120, 80, 60, 45, 20, 15

    考慮

    χ² = ∑(Oi - Ei)²/Ei = (160 - 150)²/150 + (120 - 100)²/100 + ... + (15 - 25)²/25

    2015-05-31 02:24:38 補充:

    若計出的 χ² > 12.59 則 NOT accept the declaration of the company

    明白嗎?

    2015-06-04 13:24:41 補充:

    圖片參考:https://s.yimg.com/lo/api/res/1.2/ZQit8r6YM3UMER1b...

    1.

    degree of freedom = 組別 - 1 = 7 - 1 = 6

    (嚴格來說是 (r - 1) × (c - 1) = (2 - 1) × (7 - 1))

    2.

    對於 α = 0.05,

    Standard value of χ² 就是

    χ²(α = 0.05, df = 6) = 12.59

    查表得知。

    3.

    對於 500 balls, 30% 、20% 、15%、15% 、10%、5% and 5% 分別是

    150, 100, 75, 75, 50, 25, 25 個球

    這些是 Ei

    而 Oi 分別是 160, 120, 80, 60, 45, 20, 15

    考慮

    χ² = ∑(Oi - Ei)²/Ei

    = (160 - 150)²/150 + (120 - 100)²/100 + ... + (15 - 25)²/25

    = 13.5

    4.

    由於 13.5 > 12.59

    (即是 test statistic > critical value)

    因此, 拒絕 (reject) H₀: 百分比為所列出那些

    即是, NOT accept the declaration of the company.

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