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Statistical help 1題 ... 第二

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Question 3:(c) A survey was conducted to investigate opinions about global warming. The respondents were asked to select what they expect is the cause of global warming, and the results are given in the table below.Human activityMale 314 Female 308 Natural patternsMale 146 Female 162... 顯示更多 Question 3: (c) A survey was conducted to investigate opinions about global warming. The respondents were asked to select what they expect is the cause of global warming, and the results are given in the table below. Human activity Male 314 Female 308 Natural patterns Male 146 Female 162 Don’t know Male 44 Female 46 At the 0.05 level of significance, is there evidence of a significant relationship between gender and the expected cause of global warming? (12 marks)

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以下用獨立性檢定 : H0 : 獨立 H1 : 不獨立 df = (列數-1)(行數-1) = (2-1)(3-1) = 1*2 = 2 臨界值 = χ^2 0.05(2) = 5.99 (查卡方分配表) 列出觀察值o , 再分別計算行列總合,結果如下表: 圖片參考：http://imgcld.yimg.com/8/n/AC09299269/o/20131210142547.jpg 再計算理論值eij = 第i列總合 * 第j行總合 / 行列總合 e11 = R1 * C1 / 1020 = 504*622/1020 ≒ 307.3412 e12 = R1 * C2 / 1020 = 504*308/1020 ≒ 152.1882 其餘eij計算仿照以上方法,結果如下表 : 圖片參考：http://imgcld.yimg.com/8/n/AC09299269/o/20131210142613.jpg 再計算各行列的 (e-o)^2 / e R1C1 : (307.3412-314)^2/307.3142 ≒ 0.1443 R1C2 : (152.1882-146)^2/152.1882 ≒ 0.2516 其餘列行計算仿照以上方法,結果如下表 : 圖片參考：http://imgcld.yimg.com/8/n/AC09299269/o/20131210142639.jpg 檢定的統計量 = Σ (e-o)^2 / e = 0.1443+0.2516+.....+0.0049 ≒0.792 檢定的統計量 = 0.792 < 5.99 = 臨界值故不拒絕H0,即獨立,無關聯 Ans: 無明顯證據可證明性別與對於全球暖化原因的見解有關聯. There is no evidence of a significant relationship between gender and the expected cause of global warming

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