Critical-Value|Critical-Value Approach to Hypothesis Testing

 

9.2 Critical-Value Approach to Hypothesis Testing

example:

对于mean 值 275 的假设:

Critical-Value|Critical-Value Approach to Hypothesis Testing

有一个关于sample mean的distribution:

已知population 标准差和sample size=25的情况下:

Critical-Value|Critical-Value Approach to Hypothesis Testing

标准型Z为:

Critical-Value|Critical-Value Approach to Hypothesis Testing

其中,significant level=5%,已知的mean 即为Ho假设中的值且population 标准差已经提供

存在这样的mean distribution:

Critical-Value|Critical-Value Approach to Hypothesis Testing

 

通过term 解释得到:

Critical-Value|Critical-Value Approach to Hypothesis Testing

 

 Critical-Value|Critical-Value Approach to Hypothesis Testing

 

 

 

 Critical-Value|Critical-Value Approach to Hypothesis Testing

Critical-Value|Critical-Value Approach to Hypothesis Testing

Obtaining Critical Values

此时重新理解significant level:即前提是已知H0为真,但是由于sample 问题导致z值落入reject region,此时的 significant level 为由于由于sample 问题导致z值落入reject region 的概率

Critical-Value|Critical-Value Approach to Hypothesis Testing

Keep in mind, however, that because of the central limit theorem, the one-mean z-test will work reasonably well when the sample size is large, regardless of the distribution of the variable

 

example:

Determine the critical value(s) for a one-mean z-test at the 5% significance level(α = 0.05) if the test is

 Critical-Value|Critical-Value Approach to Hypothesis Testing

一般的:

Critical-Value|Critical-Value Approach to Hypothesis Testing

 

 常用的z分布:

Critical-Value|Critical-Value Approach to Hypothesis Testing

所以假设检验的一般步骤是:

Critical-Value|Critical-Value Approach to Hypothesis Testing

 

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