Am 23.09.2008 um 23:57 schrieb Peter Dalgaard:
For this kind of problem I'd go directly for the binomial distribution. If the actual probability is 0, this is essentially deterministic and you can look at
binom.test(0,99,p=.03, alt="less")
This means that you don't sample from the p=.03 population? Note that there is a 5 per cent chance to have 0 failures in 99 trials with p=.03.
Yes, that's what I read the task as saying: Sample from p=0.00 when the hypothesis is p=0.03. Then rejection happens with probability 1 when n
>= 99. Actually, he said that we could assume the _sample_ rate to be
0%, but that is only assured when p=0.0. (You can continue the game by looking at the probability of getting 0 failures, depending on the true p. E.g., if p=0.001, we have
> dbinom(0, 99, 0.001)
[1] 0.9056978 i.e. 90% power to detect at 5% level. And further continue into a full power analysis where you calculate the probability of a failure rate that is significantly different from 0.03 depending on p and n.)
So my task is to compare a single sample population (which should exhibit 0 successes, against an a-priori p value with the goal of asking if the sample is consistent with a p-value of that or less. My goal is to determine the number of sample points needed to state with 95% confidence that the sample is predictive at alpha=.05. The process in question should always return 0 successes but I need to know how many to test so as to make those 0 successes meaningful. If I understand you correctly Peter then the binom.test procedure with a specified p value will do. Or rather that:
binom.test(0, 99, p=0.01, alt="less", conf.level=0.99)
Exact binomial test
data: 0 and 99
number of successes = 0, number of trials = 99, p-value = 0.3697
alternative hypothesis: true probability of success is less than 0.01
99 percent confidence interval:
0.00000000 0.04545154
sample estimates:
probability of success
0
correctly informs me that at a 99% confidence interval 99 systems is
woefully inadequate.
Thanks,
Collin Lynch.
Thanks,
Collin Lynch.