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FRM一级每日一题【风险管理基础34-定量分析】假设检验

来源：高顿网校 2015-03-04

　　习题：

　　Exercise:

　　You want to test at the 0.05 level of significance that the mean price of luxury cars is greater than $80,000. A random sample of 50 cars has a mean price of $88,000. The population standard deviation is $15,000. What is the alternative hypothesis?

　　A The population mean is greater than or equal to $80,000.

　　B The population mean is less than $80,000

　　C The population mean is not equal to $80,000

　　D The population mean is greater than $80,000

　　解析：

　　Answer: D

　　Explanation: The alternate hypothesis is the statement which will be accepted if the null hypothesis is proven wrong. Therefore, we make whatever we are trying to test as the alternative hypothesis – in this case that the mean price of luxury cars is greater than $80,000, and the null hypothesis as the opposite (the mean price of luxury cars is less than or equal to $80,000). This problem is a common example of how statisticians establish hypotheses by proving that the opposite is false.

　　知识点：

　　Null Hypothesis and Alternative Hypothesis

　　Hypothesis testing is a procedure used to determine whether the hypothesis is a reasonable statement and should not be rejected, or is unreasonable and should be rejected.

　　The hypothesis to be tested is called the null hypothesis (H0) while the other one is called alternative hypothesis (H1) that holds if the null does not.
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