作者air11 (iNCCU)
看板Math
标题Re: [统计] type II error
时间Mon Apr 25 12:59:47 2011
※ 引述《lynnabc236 (Lynn)》之铭言：
: Suppose a null hypothesis is that the population mean is greater
: than or equal to 100. Suppose further that a random sample of
: 48 items is taken and the population standard deviation is 14.
: use an alpha = 0.05 and solve for the probability of committing
: a Type II error if the population mean is mean(a) = 98.6
: 答案是0.8289，
: 我一直算到0.9xxx
: 我用0.05的z (1.645)和x=100去算的，
: 这样不对吗???
: 谢谢 >"<
H_0:μ≧100
H_1:μ<100
so RR: Z<-1.645
Xbar-μ
=>Z=------------- <-1.645
σ/sqrt(n)
=>Xbar<96.6579
By defn of type II error,
it suffices to find P(Xbar>96.6579)
Since μ=98.6, σ=14 and n=48
we get P(Z>-0.95)=P(Z<0.95)=0.8289
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