Statistic question....?

2021-03-09 1:55 am
Confidence interval is used to describe the statistical uncertainty associated with parameter estimates and therefore is an important tool for evaluating evidence. For example, let p be the proportion of the population who have disease A (i.e. p is the disease prevalence). If we randomly select N individuals from the population for testing and find that x of them have disease A, then our best estimate of p is x/N. We can use the binomial probability distribution to calculate the 95% confidence interval, which we denote by [L, U].

Please indicate whether each of the following statements is true or false.

a) After you have collected the data and done the calculation (i.e. [L, U] has been numerically evaluated), there is a 0.95 probability that the true prevalence p falls within the range of [L, U].

b) Before you collect the data, there is a 0.95 probability that the true prevalence p falls within the range of [L, U] that you will obtain.

回答 (1)

2021-03-09 7:41 am
✔ 最佳答案
a) After you have collected the data and done the calculation (i.e. [L, U] has been numerically evaluated), there is a 0.95 probability that the true prevalence p falls within the range of [L, U].

False.
資料經蒐集、整理、計算統計量而確定信賴區間之
上下限 U, L, 此時區間 [L.U] 是一確定的, 非隨機的
區間. 群體參數 p 雖然是未知的, 但也是非隨機的, 
只是無法確知 p 是否在區間 [L,U] 之內, 卻不能談
p 落在區間 [L,U] 之內的機率.
b) Before you collect the data, there is a 0.95 probability that the true prevalence p falls within the range of [L, U] that you will obtain.

True.
我們會說區間 [L,U] 是 p 的 95% 信賴區間, 正是說
在隨機抽樣之下, 這種方法建構的區間 [L,U] 有 95%
的機率能含蓋 p. 也就是說, 如果同一群體可以做無
數次重複地抽樣, 同樣大小的樣本, 同樣的計算 L, U 
的方式, 得到無數組的不同 [L,U], 這些區間有 95%
會含蓋 p, 也就是 p 有 0.95 的機率落入這樣的區間
內. 不過, 怎樣由樣本資料計算 L, U 的方法必須在
抽樣之前決定的, 而不能在得到、看過樣本資料之
後才決定怎樣計算 L, U.


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