我有一个功课问题，要求我使用R中的模拟测试置信区间的覆盖概率（作为前一个问题的一部分找到）。
我的代码试图从我的样本数据生成1000个随机样本（替换），有效地将我的原始样本作为我的新种群。随机样本与我的人口大小相同。然后我想找到每个随机样本的95％置信区间，看看有多少包含'真实均值'（在问题陈述中给出）与'总体均值'（我的原始样本的平均值）。
set.seed(1987)
iq <- rnorm(1000,91.08065,14.40393)
pop_mean <- mean(iq) #the mean of my sample is now considered the population mean
true_mean <- 100 #the true mean is 100, specified in question
sampSEs <- numeric() #create an empty vector to put the sample SEs in
sampMeans <- numeric() #create an empty vector to put the sample means in
get_conf_interval <- function(sample_measurements) {
iqSE_samp <- 15/sqrt(length(iq)) #find the SE using an sd of 15
iqMean_samp <- mean(sample_measurements) #take the mean of each sample
upper <- iqMean_samp + 1.96*iqSE_samp #find the upper bound for a 95% CI
lower <- iqMean_samp - 1.96*iqSE_samp #find the lower bound for a 95% CI
list(lower=lower, upper=upper)
}
interval_contains_true_mean <- function(interval) { #check if the interval contains the true mean
true_mean >= interval$lower && true_mean <= interval$upper
}
interval_contains_population_mean <- function(interval) { #check if the interval contains the population mean
pop_mean >= interval$lower && pop_mean <= interval$upper
}
samples <- replicate(1000, sample(iq, size = 124, replace = T)) #take 1000 samples with replacement from my iq data
for(i in 1:1000) { #for each sample taken
sampMeans[i] <- mean(samples[i]) #put the mean of it in the vector created previously
sampSEs[i] <- 15/sqrt(length(iq)) #put the SE in a vector... these are all the same bc not finding the sample sd
}
intervals <- apply(samples, FUN=get_conf_interval, MARGIN=2) #call the function to find the confidence intervals
sampMeans #just check if worked
#sampSEs #ditto
percent_intervals_with_true_mean <- mean(sapply(intervals, FUN=interval_contains_true_mean)) * 100
cat("% Intervals Containing True Mean: ", percent_intervals_with_true_mean, "%\n")
percent_intervals_with_pop_mean <- mean(sapply(intervals, FUN=interval_contains_population_mean)) * 100
cat("% Intervals Containing Population Mean: ", percent_intervals_with_pop_mean, "%")
此代码报告我的样本的0％置信区间包含真实均值。这不正确;我看过样本的意思，其中有几个是真正的意思。
1.-我有两个解决方案，第一个解决方案是逗号'mean（samples [，i]）'和
“set.seed（1987）
sigma_M = 14.40393
mu_M = 91.08065
米= 10
iq < - rnorm（m，mu_M，sigma_M）
pop_mean < - mean（iq）＃我的样本的平均值现在被认为是人口平均值
样品< - 复制（m，样品（iq，size = 4，replace = T））#take m样品，替换我的iq数据
sampSEs < - numeric（）#create一个空向量，用于放置样本SE
sampMeans < - numeric（）＃创建一个空向量以放入样本均值
for（i in 1：m）{#for each samples
sampMeans [i] < - mean（samples [，i]）#put在先前创建的向量中的平均值
sampSEs [i] < - 15 / sqrt（length（iq））#put在向量中的SE ...这些都是相同的bc没有找到样本sd}
get_conf_interval < - function（sample_measurements）{
iqSE_samp < - 15 / sqrt（length（iq））＃使用15的sd查找SE
iqMean_samp < - mean（sample_measurements）#take每个样本的平均值
upper < - iqMean_samp + 1.96 * iqSE_samp #find 95％CI的上限
lower < - iqMean_samp - 1.96 * iqSE_samp #find 95％CI的下限
列表（lower = lower，upper = upper）}
interval_contains_population_mean < - function（interval）{#check if interval是否包含总体均值
pop mean> = interval $ lower和pop mean <= interval $ upper}
interval < - apply（samples，FUN = get_conf_interval，MARGIN = 2）#call函数查找置信区间
sampMeans #just检查是否有效
percent_intervals_with_pop_mean < - mean（sapply（interval，FUN = interval_contains_population_mean））* 100
cat（“包含人口的％间隔平均值：”，percent_intervals_with_pop_mean，“％”）'
2.-第二个解决方案是更改代码，但我只做'pop_mean'人口平均值（并计算标准偏差）
“set.seed（1987）
sigma_M = 14.40393
mu_M = 91.08065
米= 10
iq < - rnorm（m，mu_M，sigma_M）
pop_mean < - mean（iq）＃我的样本的平均值现在被认为是人口平均值
样品< - 复制（m，样品（iq，size = 4，replace = T））#take m样品，替换我的iq数据
sampMeans = apply（样本，2，意思）
iqSE_samp < - 15 / sqrt（length（iq））＃使用15的sd查找SE
iqMean_samp < - sampMeans #take每个样本的平均值
upper < - iqMean_samp + 1.96 * iqSE_samp #find 95％CI的上限
lower < - iqMean_samp - 1.96 * iqSE_samp #find 95％CI的下限
interval = cbind（lower，upper）
percent_intervals_with_pop_mean = mean（apply（interval，1，findInterval，x = pop_mean）== 1）* 100
cat（“包含人口的％间隔平均值：”，percent_intervals_with_pop_mean，“％”）'
而决赛对我来说是80％