統計推論：已知母體標準差：基本計算 #2

已知：

求算：

• 檢定統計量 （Test Statistic）

• p-value

• 在顯著水準 α = 0.05 下，假設檢定如何。

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 <- 25.2 myMean2 <- 22.8 myStdDeviation1 <- 5.2 myStdDeviation2 <- 6.0 myNumOfSample1 <- 40 myNumOfSample2 <- 50 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) myZ <- ZOf2(myDiff, myStdDeviation1, myMean1, myNumOfSample1, myStdDeviation2, myMean2, myNumOfSample2) myZalpha <- HypothesisRightTailedTestingCriticalValue(myLevelOfSignificance) myTalpha <- HypothesisRightTailedTestingT(myLevelOfSignificance, myNumOfSampleOf2) myPvalue <- HypothesisRightTailedTestingP(myZ) HypothesisRightTailedTestingAgainstNull(myLevelOfSignificance, myZalpha, myTalpha, myZ, myPvalue)

解答：

樣本平均數= 2.4000 樣本變異數=1.3960 樣本標準差=1.1815 信任區間=0.9500 誤差界限=2.3157 [ 0.0843, 4.7157]" Reject H0, if z > 1.6449 Reject H0, if t > 1.6624 Rejected: (z=2.0313) > (Null=1.6449) Rejected: (p-value=0.0211) < (α=0.0500) Rejected: (t=2.0313) > (Null=1.6624)