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Chapter Six
Sampling Distributions
Sampling Distributions
6.1 The Sampling Distribution of the Sample Mean
6.2 The Sampling Distribution of the Sample Proportion
6.1 Sampling Distribution of the Sample Mean
The sampling distribution of the sample mean
is the probability distribution of the population of sample
means obtainable from all possible samples of size n.
Example:
Sampling Distribution of Mean
Sampling Distribution of the Sample Mean
If a random sample of size n is taken from a popula
distribution of the sample mean
is
Normal, if the sampled population is normal
Has mean
Has standard deviation
Effect of Sample Size on Sampling Distribution
Example: Gas Mileage Case
Probability that
when  = 31.
The Central Limit Theorem
For sample size n sufficiently large, the population of all possible sample means is approximately normally
distributed with
Random Sample(x1, x2, …, xn)
Population Distribution
Sampling Distribution of Sample Mean
Example:
Central Limit Theorem Simulation
Example: Effect of Sample Size
The larger the sample size, the more nearly normally distributed is the population of all possible sample means.
6.2 Sampling Distribution of Sample Proportion
is
Approximately normal, if n is large.
Has mean
Has standard deviation
Sampling Distributions
6.1
The Sampling Distribution of the Sample Mean
6.2
The Sampling Distribution of the Sample Proportion
Chapter Six / 第六章
Sampling Distributions / 抽樣分佈
Sampling Distributions / 抽樣分佈
6.1 The Sampling Distribution of the Sample Mean / 6.1 ，樣品的抽樣分佈意謂
6.2 The Sampling Distribution of the Sample Proportion / 6.2 ，樣品的抽樣分佈比例 /
6.1 Sampling Distribution of the Sample Mean / 6.1 ，樣品的抽樣分佈意謂
The sampling distribution of the sample mean is the probability distribution of the population of sample means
obtainable from all possible samples of size n. / 樣品平均數的抽樣分佈是意謂的樣品的人口的概率分布可獲得的
從規模 n 的所有合理樣品。 /
Example: Sampling Distribution of Mean / 例子: 平均數的抽樣分佈 /
Sampling Distribution of the Sample Mean / 樣品的抽樣分佈意謂
If a random sample of size n is taken from a population with me
distribution of the sample mean is / 如果一個規模 n 的隨機抽樣從人口被低劣的 和標準離差
品平均數的抽樣分佈是
Normal, if the sampled population is normal / 常態,如果被抽樣調查的人口是正常的
Has mean / 有平均數
Has standard deviation / 有標準離差 /
帶 , 那麼樣
Effect of Sample Size on Sampling Distribution / 樣品數量對抽樣分佈的效果 /
Example: Gas Mileage Case / 例子: 瓦斯運費個案
Probability that when m = 31. / 機率那當 m=31. /
The Central Limit Theorem / 中心極限定理
For sample size n sufficiently large, the population of all possible sample means is approximately normally distributed
with / 因為樣品數量 n 充分地大大地，所有合理的樣品方法的人口是常態分布的大約由於
Random Sample(x1, x2, …, xn) / 隨機抽樣 (x 1 ， x 2 ，…, xn)
Population Distribution / 總體分布
Sampling Distribution of Sample Mean / 樣品平均數的抽樣分佈 /
Example: Central Limit Theorem Simulation / 例子: 中心極限定理模擬 /
Example: Effect of Sample Size / 例子: 樣品數量的效果
The larger the sample size, the more nearly normally distributed is the population of all possible sample means. / 那比
較大的樣品數量, 那更幾乎常態分布是所有合理的樣品方法的人口。 /
6.2 Sampling Distribution of Sample Proportion / 6.2 ，樣品的抽樣分佈比例
/
如果一個規模 n 的隨機抽樣從人口
被帶 , 那麼樣品比例的抽樣分佈是
Approximately normal, if n is large. / 約計正常, 如果 n 是大的。
Has mean / 有平均數
Has standard deviation / 有標準離差 /
Sampling Distributions / 抽樣分佈
6.1 The Sampling Distribution of the Sample Mean / 6.1 ，樣品的抽樣分佈意謂
6.2 / 6.2 The Sampling Distribution of the Sample Proportion / 樣品的抽樣分佈比例