The `pt`

and `qt`

will give you the *p*-value and critical value from the *t*-distribution, respectively.

Critical value for p = 0.05, degrees of freedom = 10

qt(0.025, df = 10)

## [1] -2.228139

p-value for a critical value of 2, degrees of freedom = 10

pt(2, df=10)

## [1] 0.963306

The `t.test`

function will calculate a null hyphothesis test using the *t*-distribution.

t.test(Math.SAT ~ Sex, data = sat)

##
## Welch Two Sample t-test
##
## data: Math.SAT by Sex
## t = -1.9117, df = 158.01, p-value = 0.05773
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -59.3527145 0.9685682
## sample estimates:
## mean in group F mean in group M
## 597.6829 626.8750