# 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?

### 1 個解答

• 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：

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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