# Interpretation about a result from 2-sample t test obtained from R studio

I am trying to comparing the means of two samples and here is the output of my t test:

>t.test(Hrs_female,Hrs_male, conf.level = 0.95, alternative = "greater")
Welch Two Sample t-test
data:  Hrs_female and Hrs_male
t = -0.20031, df = 57.848, p-value = 0.579
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
-0.93453      Inf
sample estimates:
mean of x mean of y
3.966667  4.066667


How do I interpret such a 95% confidence interval with an upper bound of Inf? Does it mean my sample size is not large enough?

Thank you!

You have set the argument alternative = "greater" for a one sided test. That is why either Inf or -Inf is the natural border, you requested. Here an example with a large number of cases:

> t.test(rnorm(20000), rnorm(20000), alternative = "less")

Welch Two Sample t-test

data:  rnorm(20000) and rnorm(20000)
t = -1.139, df = 39998, p-value =
0.1274
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf 0.00504815
sample estimates:
mean of x    mean of y
-0.008239926  0.003125650


or, to demonstrate positive Inf:

> t.test(rnorm(20000), rnorm(20000), alternative = "greater")

Welch Two Sample t-test

data:  rnorm(20000) and rnorm(20000)
t = 1.368, df = 39998, p-value = 0.08565
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
-0.002771267          Inf
sample estimates:
mean of x    mean of y
0.008055759 -0.005638076


So you see, large $n$ has nothing to do with it, only the one-sided test.

• I am trying to interpret what it means when you have either -Inf or Inf in the confidence interval. Not because the alternative is less or greater or two.sided. Nov 24 '17 at 7:14
• In a two sided alternative, you are basically asking, whether 0 is outside the confidence interval. In a one sided alternative, you ask, whether there is a 0 on one specific side of the confidence interval. It is therefore sensible, to construct a one sided confidence interval and extend the other side to plus or minus$\infty$. Nov 24 '17 at 7:17
• This is a two sample t test. So I am really not into the type of alternatives I am looking at. For now, I want to understand why the lower bound or upper bound is Inf. Nov 24 '17 at 7:20
• If you are not into the type of alternatives, then just call the t.test function with the standard alternative "two.sided" and the function will give you a confidence interval, that does not include Inf`. Nov 24 '17 at 7:24