某遊戲女性玩家數超過平均值之假設檢定
場景:
根據統計某遊戲女性玩家佔 20%。
抽樣調查 400 位玩家中,有 100 位為女性。
顯著水準為 0.05。
問題:
是否女性玩家比例高於 20%?
GNU R:
# 假設檢定 source("Statistics.R") ###################################################################################################### # 分析 (p367) # H0: μ <= 0.2 # Ha: μ > 0.2 # 已知 myPopulationMean <- 0.2 mySampleSize <- 400 mySampleOfInterest <- 100 myLevelOfSignificance <- 0.05 # 求算 mySampleMean <- mySampleProportion <- mySampleOfInterest / mySampleSize myPopulationProportionStdDeviation <- HypothesisTestingPopulationProportionStdDeviation(myPopulationMean, mySampleSize) myZalpha <- HypothesisRightTailedTestingCriticalValue(myLevelOfSignificance) myTalpha <- HypothesisRightTailedTestingT(myLevelOfSignificance, mySampleSize - 1) myZvalue <- HypothesisTestingGetZfromSampleProportion(myPopulationMean, myPopulationProportionStdDeviation, mySampleMean) myPvalue <- HypothesisRightTailedTestingP(myZvalue) HypothesisRightTailedTestingAgainstNull(myLevelOfSignificance, myZalpha, myTalpha, myZvalue, myPvalue)
解答:
# Reject H0, if z > 1.6449" # Reject H0, if t > 1.6487" # Rejected: (z=2.5000) > (Null=1.6449)" # Rejected: (p-value=0.0062) < (α=0.0500)" # Rejected: (t=2.5000) > (Null=1.6487)"