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数据集 anthrop.csv 包含中间手指的长度和高度
N=3000 名罪犯。我们将此数据集视为大小为 N=3000 的总体。你
将选择 n=200 的随机样本并计算以下内容:

(a) 根据 n=200 受试者的简单随机样本估计平均身高
及其标准误。找到一个 95% 的置信区间。

(b) 确定绝对误差最多为 2 英寸所需的样本量。
如果您将当前的 n=200 样本视为一个试点样本,您会得到

(c) 使用nger计算平均高度与其标准误差的比率估计
长度作为辅助变量。计算 95% 的置信区间。

(d) 重复样本量确定,但这次是为比率估计。

(e) 重复估计平均身高,但使用回归估计并找出

(f) 在标准误差的基础上比较平均高度 ySRS, yr, yreg。哪一个

(g) 比较比率和回归估计。你觉得哪个更合适
Wèntí 1

The data set anthrop.csv contains the length of the middle nger and height of
N=3000 criminals. We will treat this data set as a population of size N=3000. You
will select a random sample of n=200 and calculate the following:

(a) Estimate the average height based on a simple random sample of n=200 subjects
and its standard error. Find a 95% con dence interval.

(b) Determine the sample size necessary to have an absolute error of at most 2 inches.
Use the whole data set to calculate the variance and compare the estimate of n
you get if you were to treat your current sample of n=200 as a pilot sample for a
future survey.

(c) Calculate the ratio estimate of average height and its standad error using nger
length as the auxiliary variable. Calculate a 95% con dence interval.

(d) Repeat the sample size determination but this time for the ratio estimate.

(e) Repeat estimation of average height but use a regression estimate and nd the
standard error.

(f) Compare average height  ySRS,  yr,  yreg on the basis of standard error. Which
estimate do you prefer and why?

(g) Compare ratio and regression estimate. Which one do you believe is more appro-
priate here and why. Use plots as necessary to support your argument.
Note: you are each requested to select your own random sample. If there are two
identical answers it will be considered cheating. The probability of this happening is so
small as to be practically zero.


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