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。

  • 信心區間為 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)) } ######################################################## # 3: 樣本數 < 30 # 已知 mySample1 <- c(10, 12, 9, 7, 7, 9) mySample2 <- c(8, 8, 6, 7, 4, 9) myConfidenceInterval <- 0.95 # 資料準備 mySampleSize <- c(length(mySample1), length(mySample2)) mySampleMean <- c(Mean(mySample1), Mean(mySample2)) mySampleStdDeviation <- c(StdDeviation(mySample1, TRUE), StdDeviation(mySample2, TRUE)) 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]) myVarianceOf2 <- PooledVarianceOf2(mySampleData$Variance[1], mySampleData$Size[1], mySampleData$Variance[2], mySampleData$Size[2]) myStdDeviationOf2 <- PooledStdDeviationOf2(mySampleData$Variance[1], mySampleData$Size[1], mySampleData$Variance[2], mySampleData$Size[2]) myMarginError <- PooledMarginErrorOf2(mySampleData$Variance[1], mySampleData$Size[1],

mySampleData$Variance[2], mySampleData$Size[2], myConfidenceInterval) MarginErrorPrintOutOf2(myMeanOf2, myVarianceOf2, myStdDeviationOf2, myConfidenceInterval, myMarginError)

解答：

樣本平均數= 2.0000 樣本變異數=3.4000 樣本標準差=1.0646 信任區間=0.9500 誤差界限=2.3720 [ -0.3720, 4.3720]

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