兩地區加油站油價假設檢定計算

場景：

問題 ：

• 兩地區平均油價差異點估計如何 （Point Estimate）

• 在信任區間 0.95 下：

  • 平均值範圍如何。

  • 誤差界限如何。

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)) } ######################################################## myDiff <- 0 myMean1 <- 2.04 myMean2 <- 1.72 myStdDeviation1 <- 0.10 myStdDeviation2 <- 0.08 myNumOfSample1 <- 40 myNumOfSample2 <- 35 myConfidenceLevel <- 0.95 myLevelOfSignificance <- 1 - myConfidenceLevel myMeanOf2 <- myMean1 - myMean2 myStdDeviationOf2 <- StdDeviationOf2(myStdDeviation1, myNumOfSample1, myStdDeviation2, myNumOfSample2) myNumOfSampleOf2 <- myNumOfSample1 + myNumOfSample2 - 2 myMarginErrorOfKnownStdDeviationOf2 <- MarginErrorOfKnownStdDeviationOf2(myStdDeviationOf2, myConfidenceLevel) MarginErrorPrintOutOf2(myMeanOf2, myStdDeviationOf2 ^ 2, myStdDeviationOf2, myConfidenceLevel, myMarginErrorOfKnownStdDeviationOf2) myZalpha <- HypothesisRightTailedTestingCriticalValue(myLevelOfSignificance) myTalpha <- HypothesisRightTailedTestingT(myLevelOfSignificance, myNumOfSampleOf2) myZ <- ZOf2(myDiff, myStdDeviation1, myMean1, myNumOfSample1, myStdDeviation2, myMean2, myNumOfSample2) myPvalue <- HypothesisRightTailedTestingP(myZ) HypothesisRightTailedTestingAgainstNull(myLevelOfSignificance, myZalpha, myTalpha, myZ, myPvalue)

解答：

樣本平均數= 0.3200 樣本變異數=0.0004 樣本標準差=0.0208 信任區間=0.9500 誤差界限=0.0408 [ 0.2792, 0.3608] Reject H0, if z > 1.6449 Reject H0, if t > 1.6660 Rejected: (z=15.3808) > (Null=1.6449) Rejected: (p-value=0.0000) < (α=0.0500) Rejected: (t=15.3808) > (Null=1.6660)