mini 發問時間： 教育與參考考試 · 10 年前

# 統計學試題20點

(一)Stress Test For a group of 10men subjected to a stress situation,the mean number of heartbeats per minute was 126,and the standard deviation was 4.Find the 95% confidence interval of the true mean. (二)Widows A recent study indicated that 29% of the 100 women over age 55 in the study were widows.a. How large a sample mus you take to be 90% confident that the estimate is within 0.05of the true proportion of women over age 55 who are widows?b. If no estimate of the sample proportion is available how large should the sample be?

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您好，舒凡很高興提為您說明信賴區間的問題 Stress Test For a group of 10men subjected to a stress situation,the mean number of heartbeats per minute was 126,and the standard deviation was 4.Find the 95% confidence interval of the true mean.此題是找了10個人的心跳，平均126，標準差4，求95%的信賴區間(CI)估計的標準差=取樣的標準差/樣本數開根號Z(0.025)=1.96CI=126±Z((1-95%)/2)*σ/√n=126±1.96*4/√10=126±2.48=(123.52~128.48) (二)Widows A recent study indicated that 29% of the 100 women over age 55 in the study were widows.WidowsA指出55歲以上在學的婦女，有29%是寡婦a. How large a sample mus you take to be 90% confident that the estimate is within 0.05of the true proportion of women over age 55 who are widows?如果建立90%的信賴區間，誤差要在真實比例0.05之內，我們要抽樣多少人?CI單邊範圍=0.05=Z(0.1/2)*估計的標準差Z(0.1/2)=1.645估計的標準差=√(p*(1-p)/n)= √(0.29*0.71/n)=0.4537/√n0.05=1.645*0.4547/√nN=(1.645*0.4547/0.05)^2=223.79取224b. If no estimate of the sample proportion is available how large should the sample be?如果不知道樣本比例，那應該抽樣多少若不知樣本比例分配，就假設是比例0.5。估計的標準差==√(p*(1-p)/n)= √(0.5*0.5/n)=0.5/√n0.05=2*1.645*0.5/√nN=(1.645*0.57/0.05)^2=270.6 取271