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# 急解~超簡單統計初階題目(20點)

1. Toss a coin 50 times and keep track of the results. Is the number of heads that appears close to the number that is predicted?

2. Toss five coins and write down the number of heads that appear. Repeat this process 50 times and then compare the observed frequencies to the probabilities.

3. Suppose you flip a coin 100 times and you want to test the hypothesis that the coin is fair, making sure that there is less than a 5 percent chance of erroneously rejecting the fair coin hypothesis. How wide should the zone of acceptance be? How wide should the zone be if you flip the coin 5 times? How wide should the zone be if you flip the coin 10 times?

4. Suppose a friend has tossed two dice, one blue and one red. You are told the total of the two numbers appearing on the dice but not the individual numbers. You want to test the hypothesis that the blue die shows 3, with only a 5 percent chance of a type 1 error. What should our testing procedure be?

5. (This one might take a while.) Flip a coin 20 times. Decide whether to accept or reject the hypothesis that the coin is fair, based on what we did in this chapter. Now repeat this procedure 100 times. How many times did you accept the hypothesis?

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State the null hypothesis and the alternative hypothesis in the following cases:

6. You want to see if cars made on Monday have more defects than cars made on other days.

7. You want to see if football teams that mostly run the football win more on the average than teams that mostly throw the football.

8. You want to see if people who drink coffee without caffeine are healthier than people who drink regular coffee.

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• 1 0 年前
最佳解答

1.投擲一枚硬幣50次並記錄下來，人頭面出現的次數是否接近你估計的數字？50*1/2＝25

2.投擲5枚硬幣並記錄人頭面出現的次數，重複此步驟50次然後比較其出現機率？

3.假設你投擲硬幣100次，你要檢定正反面出現的機率相同之假設，確定推翻假設（正反面出現機率相同）所犯的錯誤小於5％，那麼接受假設的區域為何？同理，如果你是投擲硬幣5次，上述區域為何？若是投擲10次，區域又為何？（1）0.5+(-)1.96*√(0.5*0.5/100)，其餘同理

4.假設一位朋友投擲一個藍色及一個紅色骰子，你被告知兩者出現的總數，但沒有其個別數字，要檢定假設藍骰出現3次且犯第一型錯誤之機率為5％，檢定步驟為何？-----不知道這要檢定啥？n為投擲次數

p(x=3)=[n!/3!*(n-3)!]0.5^3*0.5^n-3

5.丟一枚硬幣20次，請決定要接受假設（正反面出現的機率相同）或是推翻假設？-依本章所學。另外重複此步驟100次，你接受假設幾次？

------------照以下例子寫出其虛無假設及對立假設-----------------

6.星期一製造的車子，缺陷比其他天製造的來的多

null hypothesis：The defects of cars which made on Monday equal to other days

alternative hypothesis ：cars made on Monday have more defects than cars made on other days

7.以跑為主的足球隊，贏的次數平均比以投擲為主的多—同理

8.喝無咖啡因咖啡的人比喝一般咖啡的人健康—同理

2006-04-26 06:40:57 補充：

抱歉第9行改為

p(x=3)=[n!/3!/n-3)!]*0.5^3*0.5^(n-3)

不仔細是我的錯

參考資料： 嘎嘎嘎說的,嘎嘎嘎也說自己該睡了
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• 匿名使用者
6 年前

到下面的網址看看吧

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• 1 0 年前

1. 擲銅幣50次並且跟蹤結果。  是接近於被預言的數目出現的頭的數量嗎？ 2. 扔5 枚硬幣並且寫下出現的頭的數量。  重複這個過程50次然後把被觀察的頻率比作可能發生的事件。 3. 假定你用指頭彈一枚硬幣100次，你想要測試假說， 硬幣是應得的，保證有少於一個錯誤拒絕應得的硬幣假說的百分之5的機會。  接受的區域應該是多寬？  如果你用指頭彈硬幣5次，區域應該是多寬？  如果你用指頭彈硬幣10次，區域應該是多寬？ 4. 假定一朋友扔二骰子，藍色的一和一紅。  你被告訴在這個骰子上出現的兩數目的總數但不是個別的數目。  你想測試假說藍色死顯示3，帶有只一個一個1 類型錯誤的百分之5的機會。  我們的測試過程應該是什麼？ 5. (這個可以帶一會兒.)  用指頭彈一硬幣20次。  決定是接受還是拒絕硬幣是應得，基於我們在這章裡做的的的假說。  現下重複這程式100次。  你接受假說多少次？ 在下列情況裡說明零假設和備選假設︰ 6. 你想要看看是否在星期一做的汽車有比汽車在其他天做的更多的缺陷。 7. 你想要看看主要跑的足球隊足球贏得比比主要投足球的隊平均如果。 8. 你想要看看是否沒有茶鹼而喝咖啡的人們比喝有規律的咖啡的人們健康。

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