Statistical hypothesis ...20－bgdwze3的部落格

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Statistical hypothesis ...20

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發問:

(a) The "Beauty" industry in Hong Kong estimated that at least 40% of local women were really concerned about their appearance and beauty. To check this market size estimation, a random sample was taken, and it was found that 85 of 200 randomly and independently selected women were actually not... 顯示更多 (a) The “Beauty” industry in Hong Kong estimated that at least 40% of local women were really concerned about their appearance and beauty. To check this market size estimation, a random sample was taken, and it was found that 85 of 200 randomly and independently selected women were actually not satisfied with their appearance and beauty. At the 0.05 level of significance, is there any evidence to support the industry’s estimation? (8 marks) (b) According to a recent political survey in Hong Kong, the following table showed the preference of political parties of 300 randomly and independently selected citizens, (including 100 workers, 150 professionals, and 50 business owners) in the next election. Workers Professional Business Owners Party A 55 75 25 Party B 22 30 12 Party C 23 45 13 At the 0.05 level of significance, is there any evidence that the proportions of political party preference among the three groups are the same? (12 marks) (c) What is significance level and what is its role in hypothesis testing? (5 marks

最佳解答:

(a) H0 : p ≦ 0.4 H1 : p > 0.4 臨界值 = Z 0.05 = 1.645 確認是否可用常態檢定: 0.4 ± 3 √(0.4*0.6/200) = 0.4 ± 3*0.035 = 0.295 ~ 0.505 不含0與1,故可用常態檢定. 檢定的統計量 = ( 85/200 - 0.4 ) / √(0.4*0.6/200) = ( 0.425 - 0.4 ) / 0.035 ≒ 0.714
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