Chapter 6 Example 2.2
We use the differences Standard minus Ergonomic for the runstitching data.> library(cfcdae)
> data(RunStitch)
> differences <- RunStitch[,"Standard"] - RunStitch[,"Ergonomic"]
> differences
[1] 1.03 -0.04 0.26 0.30 -0.97 0.04 -0.57 1.75 0.01 0.42 0.45 -0.80
[13] 0.39 0.25 0.18 0.95 -0.18 0.71 0.42 0.43 -0.48 -1.08 -0.57 1.10
[25] 0.27 -0.45 0.62 0.21 -0.21 0.82
We want to examine both the hypothesis of Mr. Skeptical (\(\mu = 0\))
and Mr. Enthusiastic (\(\mu = 0.5\)). The t.test()
function does exactly
what we need. In addition, we ask for a 95% confidence interval
for the mean.
> t.test(differences,mu=0,conf.level=.95)
One Sample t-test
data: differences
t = 1.49, df = 29, p-value = 0.147
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
-0.06532811 0.41599478
sample estimates:
mean of x
0.1753333
> t.test(differences,mu=0.5,conf.level=.95)
One Sample t-test
data: differences
t = -2.7591, df = 29, p-value = 0.009934
alternative hypothesis: true mean is not equal to 0.5
95 percent confidence interval:
-0.06532811 0.41599478
sample estimates:
mean of x
0.1753333
In either case, the 95% confidence interval is the same (-.065, .416), as the confidence interval does not depend on a null hypothesis for the mean. This interval includes 0 but does not include .5 (the 99% interval goes right up to .5).