chapter4.ppt

Chapter 4
Confidence Intervals
置信区间
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Chapter Outline
Confidence Intervals for the Mean (Large Samples)
Confidence Intervals for the Mean (Small  Samples)
Confidence Intervals for Population Proportions
Confidence Intervals for Variance and Standard  Deviation
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Section
Confidence Intervals for the Mean (Large Samples)
大样本情况下总体均值的区间估计
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Section Objectives
掌握点估计point estimate和估计误差 margin of error
会构建总体均值的置信区间
当估计总体均值μ时,求解必须的样本容量minimum sample size
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导入
你想要估计我班同学的平均年龄average age.
方法:随机抽取了50名同学,. 通过这50名同学的样本,. 此为点估计
Point Estimate
A single value estimate for a population parameter
Most unbiased point estimate of the population mean μ is the sample mean
Estimator估计量:用来估计总体参数的统计量。
总体均值的最佳估计量?
总值比例的最佳估计量?
总体方差的最佳估计量?
优良估计量的三大标准
无偏性Unbiased.
有效性Relatively efficient. 对同一总体参数的两个无偏估计量,有更小标准差的估计量更有效.
一致性Consistent. 随着样本容量的增大,点估计量的值越来越接近被估计总体的参数.
Interval Estimate区间估计
Interval estimate
An interval, or range of values, used to estimate a population parameter.
Point estimate
•

此区间可能包括也可能不包括总体参数的真值。
How confident do we want to be that the interval estimate contains the population mean μ?
( )
Interval estimate
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Level of Confidence置信水平
Level of confidence c
指的是,如果将构造置信区间的步骤重复多次,置信区间中包含总体参数真值的次数所占的比例.
z
z = 0
-zc
zc
Critical values
½(1 – c)
½(1 – c)
c is the area under the standard normal curve between the critical values.
The remaining area in the tails is 1 – c .
c
Use the Standard Normal Table to find the corresponding z-scores.
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zc
Level of Confidence
mon are used: 90%, 95%, and 99%.
If the level of confidence is 90%, this means that we are 90% confident that the interval contains the population mean μ.
The corresponding z-scores are +.
z
z = 0
zc
c =
½(1 – c) =
½(1 – c) =