I am designing a study to demonstrate that a diagnostic medical device is more sensitive than a fixed performance goal of 70%. Currently I am attempting to determine the appropriate sample size. My hypotheses are:
H0: u <= u0
H1: u > u0
u - Sensitivity of the device under test
u0 - Performance goal sensitivity = 70%
So typically we would observe a bunch of subjects with the target disease (all positive for the disease) and get a positive (+) or negative (-) test result from the test device.
Say we take 36 subjects and get 31 + results with the test. We could use the binomial test to determine the one tailed test result:
binom.test(31, 36, (7/10), alternative ="greater")
However, in my case I will be obtaining a Sensitivity of the test from each subject and then estimating the mean and variance Sensitivity of the test device from my group of subjects.
Subject - Test Result
1 - 85%
2 - 77%
3 - 50%
4 - 55%
5 - 90%
n - Xi
What would be the appropriate test statistic for this design?