※ 引述《maxdi.bbs@ptt.cc》之銘言：
> suppose the random variable X is normally distributed with meanμx and
> variance 400,A random sample with 36 observations is drawn to test whether
> of X is 100.Please answer the following questions.
> 1.Suppose the statistical inference rule is set to reject the null hypothesis
> whether the sample mean is greater then 106 or less then 94.What is the
> probability of type I error committed with the inference rule?
Test rule:
Reject H0 if and only if Xbar>106 or Xbar<94
即
Not reject H0 iff. Xbar≦106 and Xbar≧94
Tyep 1 error: reject H0 while H0 is true.
Type II error: not reject H0 while H0 is false.
The null hypothesis (H0) is
whether the mean μ of X is 100. (μX 省略 X)
H0 is true <==> μ = 100.
故計算 the probability of type I error
當然在 μ=100 時計算. 而要計算機率的 event 是
"reject H0", 也就是 Xbar>106 or Xbar<94.
> (a)0.929 (b)0.072 (c)0.833 (d)0.167 (e)None of the above
> 2.following questions 1,What is the probability of type II error committed
> with the inference rule when the true mean is 99?
Tyep II error 指 H0 不成立時卻 not reject H0, 即
μ≠100 但不 rehect H0.
因此, 計算 the probability of type II error 當然是
在 μ≠100 時. 而要計算機率的事件是 "not reject H0",
也就是 "94≦Xbar≦106". 但 μ≠100 有無限多個值,計
算機率必須取特定的值. 題目已明言
"when the true mean is 99"
當然是在 μ=99 時計算上述事件的機率.
> 第一題用誤差等於 Xbar正負Z(α/2)xσ√n 算α=0.072
> 但是第二題我就不知道怎麼算β
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