旅客對不同機場滿意度調查誤差界限計算

場景：

• • 旅客對 Miami 及 Los Angeles 機場滿意度調查，資料如附件檔。

問題：

• • 求算信心區間為 95% 下之誤差界限。（樣本標準誤差=0.4541 誤差界限=0.8901）

  • 求算平均價格之點估計。（[-0.5101, 1.2701]）

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)) } ######################################################## # 6: 樣本數 > 30 # 已知 myConfidenceInterval <- 0.95 # 資料準備 mySampleRowData <- read.table(file="Statistical-Inference-6.dat", header=TRUE) mySampleSize <- length(mySampleRowData$Miami) mySampleMean <- c(Mean(mySampleRowData$LosAngeles), Mean(mySampleRowData$Miami)) mySampleStdDeviation <- c(StdDeviation(mySampleRowData$LosAngeles, TRUE), StdDeviation(mySampleRowData$Miami, TRUE)) mySampleVariance <- mySampleStdDeviation ^ 2 mySampleData <- data.frame(mySampleSize, mySampleMean, mySampleVariance, mySampleStdDeviation, row.names=mySampleNames) names(mySampleData) <- c("Size", "Mean", "Variance", "StdDeviation") print(mySampleData) print(summary(mySampleData)) # 求算 myMeanOf2 <- MeanOf2(mySampleData$Mean[1], mySampleData$Mean[2]) myStdDeviationOf2 <- StdDeviationOf2(mySampleData$StdDeviation[1], mySampleData$Size[1], mySampleData$StdDeviation[2], mySampleData$Size[2]) myVarianceOf2 <- myStdDeviationOf2 ^ 2 myMarginError <- MarginErrorOfKnownStdDeviationOf2(myStdDeviationOf2, myConfidenceInterval) MarginErrorPrintOutOf2(myMeanOf2, myVarianceOf2, myStdDeviationOf2, myConfidenceInterval, myMarginError)

解答：

Size Mean Variance StdDeviation 2000 50 6.72 5.634286 2.373665 1999 50 6.34 4.677959 2.162859 Size Mean Variance StdDeviation Min. :50 Min. :6.340 Min. :4.678 Min. :2.163 1st Qu.:50 1st Qu.:6.435 1st Qu.:4.917 1st Qu.:2.216 Median :50 Median :6.530 Median :5.156 Median :2.268 Mean :50 Mean :6.530 Mean :5.156 Mean :2.268 3rd Qu.:50 3rd Qu.:6.625 3rd Qu.:5.395 3rd Qu.:2.321 Max. :50 Max. :6.720 Max. :5.634 Max. :2.374 樣本平均數= 0.3800 樣本變異數=0.2062 樣本標準差=0.4541 信任區間=0.9500 誤差界限=0.8901 [ -0.5101, 1.2701]