樣本數 >= 30 時，不同樣本群誤差界限計算

場景：

• • 2 群樣本，樣本數 > 30。

  • 信心區間分別為 90% 及 95% 。

問題：

• • 求算誤差界限。

  • 求算平均價格之點估計。

GNU R：

source("Statistics.R") ######################################################## MarginErrorPrintOutOf2 <- function(myMeanOf2, myVarianceOf2, myStdDeviationOf2, myConfidenceInterval, myMarginError) { print(sprintf("樣本平均數=%8.4f 樣本變異數=%.4f 樣本標準差=%.4f 信任區間=%.4f 誤差界限=%.4f [%8.4f, %8.4f]", myMeanOf2, myVarianceOf2, myStdDeviationOf2, myConfidenceInterval, myMarginError, myMeanOf2-myMarginError, myMeanOf2+myMarginError)) } ######################################################## # 1: 樣本數 >= 30 # 已知 mySampleSize <- c(50, 35) mySampleMean <- c(13.6, 11.6) mySampleStdDeviation <- c(2.2, 3.0) myConfidenceInterval <- c(0.9, 0.95) # 資料準備 mySampleVariance <- mySampleStdDeviation ^ 2 mySampleNames <- c("SampleA", "SampleB") names(mySampleSize) <- mySampleNames names(mySampleMean) <- mySampleNames names(mySampleVariance) <- mySampleNames names(mySampleStdDeviation) <- mySampleNames mySampleData <- data.frame(mySampleSize, mySampleMean, mySampleVariance, mySampleStdDeviation, row.names=mySampleNames) names(mySampleData) <- c("Size", "Mean", "Variance", "StdDeviation") # 求算 myMeanOf2 <- MeanOf2(mySampleData$Mean[1], mySampleData$Mean[2]) myStdDeviationOf2 <- StdDeviationOf2(mySampleData$StdDeviation[1], mySampleData$Size[1], mySampleData$StdDeviation[2], mySampleData$Size[2]) for (myElement in c(1:2)) { myMarginError <- MarginErrorOfKnownStdDeviationOf2(myStdDeviationOf2, myConfidenceInterval[myElement]) MarginErrorPrintOutOf2(myMeanOf2, myStdDeviationOf2 ^ 2, myStdDeviationOf2, myConfidenceInterval[myElement], myMarginError) }

解答：

樣本平均數= 2.0000 樣本變異數=0.3539 樣本標準差=0.5949 信任區間=0.9000 誤差界限=0.9786 [ 1.0214, 2.9786] 樣本平均數= 2.0000 樣本變異數=0.3539 樣本標準差=0.5949 信任區間=0.9500 誤差界限=1.1660 [ 0.8340, 3.1660]