R notes for Activity 19-3
19-3 c: Visualizing Sample Data
You can read and preview the data with
BodyTemps = read.csv("/home/rebelsky/Stats115/Data/BodyTemps.csv")
summary(BodyTemps)
head(BodyTemps)
You'll note that the data have two columns: BodyTemp
and Sex. We just want the first column, which we
will select with BodyTemps$BodyTemp.
We can build a quick histogram of those data with the following command.
(Since R and Minitab make different decisions as to how to make
intervals, this may look a bit different than the sample answer.)
hist(BodyTemps$BodyTemp)
But we should certainly label the x axis
hist(BodyTemps$BodyTemp,
main="Sample Body Temperatures",
xlab="Body Temperature in Degrees F"
)
If we'd rather do a dot plot, we can use
library(BHH2, lib="/home/rebelsky/Stats115/Packages")
dotPlot(BodyTemps$BodyTemp,
main="Sample Body Temperatures",
xlab="Body Temperature in Degrees F"
)
We can create the normal probability plot with
qqnorm(BodyTemps$BodyTemp, datax=T, ylab="Body Temperature in Degrees F")
19-3 f: Computing Confidence Intervals
Since you used some form of technology to compute these confidence
intervals in activity 19-1, I'm not sure why they're asking you to do so
again. But, hey, let's cooperate. One technique is to tell R the
formula. We'll start by recording the
values we know.
x_bar = 98.249
s = .733
n = 130
We can use qt to compute t*.
Unlike the table on p. 625, qt computes the appropriate
t value given the area to the left of that t. Hence,
for a 95% confidence interval, we use .975. (Why .975? Because there's
0.025 to the right, and therefore 0.975 to the left.) As you should
recall from the reading, the degrees of freedom should be
n-1.
t_star = qt(0.975, n-1)
Now, we're ready to compute the lower bound and upper bounds of
the confidence interval using the standard formula.
ci_lower = x_bar - t_star*s/sqrt(n)
ci_upper = x_bar + t_star*s/sqrt(n)
c(ci_lower, ci_upper)
Of course, that's a lot of work. Hence, we might want to use the
built-in t.test function, which provides not
just the confidence interval, but also a lot of other data. However,
we need to work from the original data set, rather than from the mean
and standard deviation already computed from that data set. (If you
only know mean, standard deviation, and sample size, you'll need to
use the technique above.) To use the t.test
function, you also need to provide a hypothesized population
parameter (mu) and a desired confidence interval
(conf.level). While you don't need mu to compute
the confidence interval, the t-test computes more
than just the confidence interval, and therefore requires a bit more.
t.test(BodyTemps$BodyTemp, mu=98.6, conf.level=0.95)
For the other two confidence intervals, we would use
t.test(BodyTemps$BodyTemp, mu=98.6, conf.level=0.90)
t.test(BodyTemps$BodyTemp, mu=98.6, conf.level=0.99)
19-3 j: Computing Another CI
Since you don't have the original data set, you cannot use the
t.test function. Hence, you must provide
R with the formulae.
x_bar = 98.249
s = .733
n = 13
t_star = qt(0.975, n-1)
ci_lower = x_bar - t_star*s/sqrt(n)
ci_upper = x_bar + t_star*s/sqrt(n)
c(ci_lower, ci_upper)
