A 99% confidence interval estimate can be interpreted to mean that
(A)lf all possible samples are taken and confidence interval estimates are
developed, 99% of them would include the true population mean
somewhere within their interval
(B)We have 99% confidence that we have selected a sample whose interval
does include the population mean
(C)Both of the above
(D)None of the above
99% 的信賴區間估計可以解釋為
(A) 如果採集了所有可能的樣本並得出了信賴區間估計值，那麼 99% 的樣本將包括其區間內某處的真實母體平均值
(B) 我們有 99% 的信賴度認為我們選擇了一個樣本，其區間確實包含母體平均值
(C) 以上兩者
(D) 以上都不是
(台大商研)
答：(C)
For the following statements about a confidence interval (CI), which is (are)
true?
(a) The narrower the CI, the better, for the same level of confidence.
(b) The narrower the CI, the higher the confidence level.
(c) A 95% CI for the mean of population implies a .95 probability that the
mean of the population lies in that interval.
(A) (a)(b)(c)
(B) (a)(c)
(C) (a)
(E) none
(成大財金)
對於以下關於置信區間 (CI) 的陳述，哪個是（是）真的？
(a) 對於相同的信賴水平，CI 越窄越好。
(b) CI 越窄，信賴水平越高。
(c) 母體平均數的 95% CI 意味著 0.95 的機率
母體平均數位於該區間內。
答：(C) (a)
(b) CI 越窄，信賴水平越低
(c) 母體平均數的 95% CI 並非意味著 0.95 的機率母體平均數位於該區間內。相反，我們不知道母體平均數有多少機率會落在信賴區間。譬如，我們預測人類哪時候滅亡，五十年後、一百年後、一千年後甚至一億年後，當然區間估計範圍拉的越大，譬如估計一億年後人類滅亡，估計準確度就降低，所以並非區間拉的越大機率越大。The 95% confidence interval is a range of values that you can be 95% confident contains the true mean of the population.
Which of the following statements about confidence interval is true?
(A)For a certain level of confidence, we would prefer a wide confidence
interval over a narrow confidence interval because the wide confidence
interval is more likely to contain the true value of the population parameter
(B)A good confidence interval has a large width and a high level of
confidence
(C)Suppose
we construct a two-sided and a one-sided confidence intervals for
the population mean. In each case, the level of confidence is 1-a. The
lower confidence limit for the two-sided interval exceeds the lower
confidence limit for the one-sided interval
(D)Other things being equal, we could always increase sample size to reduce
the width of confidence interval
(E) None of the above answer is correct
下列關於信賴區間的說法正確的是？
(A) 對於一定的信賴水準，我們更喜歡寬信賴區間而不是窄信賴區間，因為寬信賴區間更有可能包含母體平均數的真實值
(B) 一個好的信賴區間具有較大的寬度和較高的信賴水準
(C) 假設我們為母體平均值構建了一個雙尾和一個雙尾信賴區間。 在每種情況下，信賴水準都是 1-a。 兩側區間的信賴下限超過單側區間的信賴下限
(D) 在其他條件相同的情況下，我們總是可以增加樣本量以減少置信區間的寬度
(E) 以上答案都不正確
(中正企管)
答：(D)
(A)錯，信賴區間越窄估計越精確
(B)錯，區間越窄越精確，雖然信賴水準越低區間越窄，但可靠度也會降低，估計範圍變小，並非好方法。應該增加樣本數使區間變窄，樣本越大母體參數容易穩定集中在較小範圍。
(C)兩側區間的信賴下限低於單側區間的信賴下限
一家雜誌社欲知其讀者的平均年齡,以作為雜誌內容走向的參考,根據其
對訂戶抽查所得的讀者平均年齡為 35 歲。當樣本數為 25,母體分配為常
態,樣本標準差為6歲,求該雜誌讀者平均年齡的95%信賴區間。
〈台北合經》
