珠寶店鑽石售價不同於官價之架設檢定

場景

    • 鑽石每克拉官價為 $5600 元。

    • 抽要調查芝加哥 25 家珠寶店,其鑽石每克拉售價資料如附件檔。

    • 顯著水準為 0.05。

問題

    • 是否芝加哥鑽石每克拉售價與官價不同?

GNU R

# 假設檢定 source("Statistics.R") ###################################################################################################### # 分析 (29) # H0: μ = 5600 # Ha: μ != 5600 myPopulationMean <- 5600 myLevelOfSignificance <- 0.05 # 求算 mySampleData <- read.table(file="HypothesisTesting-29.dat", header=TRUE) print(mySampleData) print(summary(mySampleData)) mySampleSize <- length(mySampleData$Price) mySampleMean <- Mean(mySampleData$Price) mySampleStdDevation <- StdDeviation(mySampleData$Price, TRUE) myZalpha <- HypothesisBothTailedTestingCriticalValue(myLevelOfSignificance) myTalpha <- HypothesisBothTailedTestingT(myLevelOfSignificance, mySampleSize - 1) myZvalue <- HypothesisTestingGetZfromSample(myPopulationMean, mySampleStdDevation, mySampleSize, mySampleMean) myPvalue <- HypothesisBothTailedTestingP(myZvalue) HypothesisBothTailedTestingAgainstNull(myLevelOfSignificance, myZalpha, myTalpha, myZvalue, myPvalue)

解答

Price 1 4620 2 6210 3 5150 4 5250 5 4840 6 6320 7 5450 8 5620 9 6140 10 5850 11 5640 12 6575 13 5940 14 5850 15 5825 16 5820 17 6850 18 6010 19 5960 20 5980 21 6330 22 5990 23 5995 24 6360 25 5300

Price Min. :4620 1st Qu.:5620 Median :5940 Mean :5835 3rd Qu.:6140 Max. :6850 Reject H0, if z < -1.9600 or z > 1.9600 Reject H0, if t < -2.0639 or t > 2.0639 Rejected: (z=2.2591) < (Null=1.9600) Rejected: (p-value=0.0239) < (α=0.0500) Rejected: (t=2.2591) < (Null=2.0639)