概率论与数理统计及其应用实验报告2
时间:2020-09-24 20:18:16 来源:勤学考试网 本文已影响 人
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《概率论与数理统计及其应用》
实 验 报 告
实验报告
1、实验名称:区间估计
2、实验性质:上机操作
3、实验目的:
理解在R语言中进行区间估计和假设验证
了解常用统计函数在 R 中的表示方法,学会在 R 中求出这些统计函数值,计算参数的置信区间
4、实验内容:
例二:
x=c(422.2,418.7,425.6,420.3,425.8,423.1,431.5,428.2,438.3,434.0,412.3,417.2,413.5,441.3,423.7)
n=length(x)
y=rnorm(15)
x=x+y
ave = mean(x)
s = sqrt(var(x))
alpha = 0.05
q = qt(1-alpha/2,(n-1))
left = ave - s*q / sqrt(n)
right = ave + s*q / sqrt(n)
result = c(left,right)
结果:
x:419.9195 417.9493 426.4449 419.4891 425.4031 424.1903 431.1452 426.1767
[9] 437.8118 433.4208 413.0695 418.5570 412.9946 443.5730 423.7255
ave:424.9247
s: 8.69103
q: 2.144787
result:置信区间为( 420.1117 , 429.7376)
例三:
x=c(86,87,56,93,84,93,75,79,81,78,79,90,68,65,87,90)
nx=length(x)
z=rnorm(16,mean=8,sd=7)
x=x+z
y=c(80,79,58,91,77,82,74,66,58,59,64,78,76,80,82,55)
z=rnorm(16,mean=8,sd=7)
y=y+z
ny=length(y)
avex = mean(x)
avey = mean(y)
sw = sqrt((nx-1)*sqrt(var(x))+(ny-1)*sqrt(var(y)))/(nx+ny-2)
alpha = 0.05
q = qt(1-alpha/2,(nx+ny-1))
left = avex - avey - sw*q / sqrt(nx+ny)
right = avex - avey + sw*q / sqrt(nx+ny)
result = c(left,right)
data.frame(diference=avex-avey,df=nx+ny-2,left,right)
结果:
x: 90.29086 108.02870 82.64284 93.24831 90.98072 102.30985 82.46135
[8] 83.12287 79.90874 84.16916 89.11274 98.68181 84.33725 70.17321
[15] 106.61700 112.62761
y: [1] 88.98278 86.45529 73.27553 109.81205 88.80518 96.26914 77.02845
[8] 79.62434 73.38286 70.33023 66.12525 83.64447 94.71065 91.23822
[15] 89.77377 72.51869
avex:91.16956 avey:83.87356
q:2.039513 sw:2.039513
result: diference df left right
7.296008 30 7.071572 7.520445
课本p221 18题
(1)
x=c(1.79,1.75,1.67,1.65,1.87,1.74,1.94,1.62,2.06,1.33,1.96,1.69,1.70)
nx=length(x)
y=c(2.39,2.51,2.86,2.56,2.29,2.49,2.36,2.58,2.62,2.41)
ny=length(y)
sx = var(x)
sy = var(y)
F = sx / sy
alpha = 0.1
q1 = qf(alpha/2,nx-1,ny-1)
q2 = qf(1-alpha/2,nx-1,ny-1)
结果:
sx: 0.0340141 sy:0q1: 0.3576058 q2:3.072947
F: 1.288359
由结果可知 F不在拒绝域内 则假设H0成立
继续检验:
avex = mean(x)
avey = mean(y)
sw = ((nx-1)*sx+(ny-1)*sy) / (nx+ny-2)
t = abs((avex-avey)/(sqrt(sw)*sqrt((1/nx)+(1/ny))))
q = qt(1-alpha/2,(nx+ny-2))
结果:
avex: 1.751538 avey: 2.507
sw: 0 t: 10.24207
q: 1.720743
故拒绝H0’,认为杂志上刊载的论文与未出版的学术报告的可理解性有显著差异
5、实验心得:
在这次实验,我体会到了如何使用R语言进行假设检验,对于假设检验和回归分析有了更深一步的了解,同时也明白了如何把一个具体问题转化为R语言中的代码进行求解。