Two studies were conducted independently to determine the sensitivity of two common COVID-19 tests. The results of the studies are provided below:

Swab Saliva

True Positives 229 95 324

False Negatives 84 57 141

313 152 465

a)

Sensitivity is defined as the ratio of the number of true (verified) positive test results to the total number of verified positive cases (note this typically requires external validation). Construct a 95% confidence interval for the sensitivity of the swab test.

b)

Note that sensitivity effectively defines the expected proportion of individuals that are infected, that will be correctly identified by the test. For every 1,000 infected people tested using the saliva test, how many would we expect to receive negative test results?

c)

Perform a hypothesis test to determine if the sensitivity of the two of tests are the same