sample size to get 99.6% confidence on a one-tailed test If I have a normally distributed population of 3.5 million elements, and I want to sample enough of them to make a statement with 99.6% confidence on a 1-tailed test, what should my sample size be?  Is 100 enough, or would it need to be significantly larger?  
 A: You can use the following R script to generate your required sample:
library(pwr)
pwr.t.test(n = SAMPLE_SIZE , d = EXPECTED_EFFECT_SIZE, sig.level = 0.004 , power = DESIRED_POWER, type = c("one.sample"), alternative = "greater"/"less")
You need to provide 3 of the 4 values (n,*d*,sig.level, and power), while making the 4th value = NULL. For example, if you wanted to see if 100 subjects is enough, you could fill in information for n, d (if you have an expected effect size, for this example d will be equal to 0.4), your significance level of 0.004 (or 99.6% CI), while leaving power as Null. Lastly, you will need to choose the direction for the one-tailed test by choosing "greater" or "less", which for this example, I chose to use "greater". The below R script will perform this calculation:
library(pwr)
pwr.t.test(n = 100 , d = 0.4, sig.level = 0.004 , power = NULL, type = c("one.sample"), alternative = greater)
Below is the generated output:
 One-sample t test power calculation 

          n = 100
          d = 0.4
  sig.level = 0.004
      power = 0.8991141
alternative = greater

As you can see in the above output, we have 89.9% power to test our null hypothesis with an expected difference in effect size of 0.4 with 99.6% confidence ($a$ = 0.004).
