Interpreting a confidence interval with a negative limit I am doing an independent samples t-test on days hospitalized for eventually deceased patients and eventually recovered patients.The problem I'm facing is that should I rule out the negative limit in the confidence interval?
t-test result in R code:
> t.test(recovered$days.hospitalised,deceased$days.hospitalised,var.equal = T)

    Two Sample t-test

data:  recovered$days.hospitalised and deceased$days.hospitalised
t = 0.60695, df = 1998, p-value = 0.544
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.7675133  1.4555133
sample estimates:
mean of x mean of y 
   30.518    30.174

The confidence interval I got was -0.76 and 1.46 as seen above from the output, which means that the days hospitalized for a recovered patients is -0.76 to 1.45 days higher than a deceased patient.
However, it seems impossible for a recovered patient to stay negative days. I'm new to statistics so bear with me. Is is correct to say that the recovered patient stayed 0 to 1.46 days longer that a deceased patient?
Please advise and thank you for reading.
 A: You may have to clarify the problem, and maybe I don't understand the variables. You did a t.test comparing the mean of recovered patients to deceased patients, and fail to reject the null that they are different. You essentially found that the mean difference between stay for patients that recover and patients that decease is anywhere from -.76 days to 1.45 days. What this means is that recovered patients seem to stay in the hospital about the same amount as decreased patients. This result is not saying that the mean recovered stay is negative, but rather that the difference between the mean recovered stay and mean deceased stay could either be negative or positive. In other words, your data cannot rule out which mean is truly higher: as you can see in the R output, the means for both are both basically $30$ days. It would absolutely be incorrect to ignore that negative part and report 0 to 1.45. 
Maybe it helps to think of another example. Suppose I sample 100 seniors from two different states and ask their ages. Because education is roughly the same in both states, seniors in both states have about the same ages. Because of random sampling noise, let's say I find that the average senior is aged 17.5 in state 1 and 17.7 in state 2. A t-test comparing the differences would certainly give me a confidence region that include negative values, because its the confidence region on the difference in means. 
