高爾夫杆數抽樣分析

場景：

• 高爾夫杆數統計如下：

問題：

• 求算樣本標準差。
• 求算樣本在 3 杆區間內之機率。

解答：

GNU R：

# 已知母體平均數，樣本數，求算樣本標準差 SampleStdDeviation <- function(populationStdDeviation, sampleSize) { myStdDeviation <- populationStdDeviation / sqrt(sampleSize) myStdDeviation } # 已知母體平均數，樣本標準差，求算樣本在某母體平均數百分比區間之機率 SampleMeanPercentageRangeProbability <- function(populationMean, sampleStdDeviation, samplePercentageRange) { sampleValueRange <- populationMean * samplePercentageRange z2 <- sampleValueRange / sampleStdDeviation z1 <- -1 * z2 p2 <- pnorm(z2) p1 <- pnorm(z1) myProbability <- p2 - p1 myProbability } # 已知母體平均數，樣本標準差，求算樣本在某母體平均數值區間之機率 SampleMeanValueRangeProbability <- function(sampleStdDeviation, sampleValueRange) { z2 <- sampleValueRange / sampleStdDeviation z1 <- -1 * z2 p2 <- pnorm(z2) p1 <- pnorm(z1) myProbability <- p2 - p1 myProbability } ############################################################################################################## populationMean <- c(95, 106) populationStdDeviation <- c(14, 14) sampleSize <- c(30, 45) sampleValueRange <- 3 sampleStdDeviation <- vector(mode="double", 2) sampleRangeProbability <- vector(mode="double", 2) sampleObjectName <- c("男性", "女性") for (mySampleObject in c(1:2)) { myStdDeviation <- SampleStdDeviation(populationStdDeviation[mySampleObject], sampleSize[mySampleObject]) myProbability <- SampleMeanValueRangeProbability(myStdDeviation, sampleValueRange) print(sprintf("%s 機率(區間=%d)=%0.3f 平均數=%3d 標準差=%3.4f", sampleObjectName[mySampleObject], sampleValueRange, myProbability, populationMean[mySampleObject], myStdDeviation)) } # warnings()