Hypothesis Test

To perform a hypothesis test for a single mean you need to use the t.test() function and specify the variable, x, the value of the population parameter, mu, and the alternative hypothesis. By default the alternative hypothesis is "two.sided", but you can also use "less", or "greater".

t.test(x = variable, mu = mu_0, alternative="less")

Confidence Interval

To calculate a confidence interval for a single mean you need to use the t.test() function and specify the variable, x, and set the confidence level, conf.level = .95. You may also set the population parameter, but it is not necessary for a hypothesis test. Adding $conf.int to the end of the t.test() function will display only the confidence interval.

t.test(x = variable, conf.level = .95)$conf.int

Example

The data for this example comes from the sleep dataset. Suppose 20 individuals recorded the amount of "extra" sleep they got on a particular weekend. Is the amount of extra sleep significantly greater than 1.5?

# Hypothesis Test
t.test(sleep$extra, mu = 1.5, alternative = "greater" )
## 
##  One Sample t-test
## 
## data:  sleep$extra
## t = 0.088648, df = 19, p-value = 0.4651
## alternative hypothesis: true mean is greater than 1.5
## 95 percent confidence interval:
##  0.7597797       Inf
## sample estimates:
## mean of x 
##      1.54
# Confidence Interval
t.test(sleep$extra, conf.level = .95 )$conf.int
## [1] 0.5955845 2.4844155
## attr(,"conf.level")
## [1] 0.95

Mathematicss, Computer Science, and Statistics Department Gustavus Adolphus College