Introduction to Statistics (MAT/SST 115.03 2008S)
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:
Sex. We just want the first column, which we
will select with
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.)
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$BodyTemp, datax=T, ylab="Body Temperature in Degrees F")
Since you used some form of technology to compute these confidence intervals in activity 19-1, I'm not sure why they're asking you to do so again. But, hey, let's cooperate. One technique is to tell R the formula. We'll start by recording the values we know.
x_bar = 98.249 s = .733 n = 130
We can use
qt to compute t*.
Unlike the table on p. 625,
qt computes the appropriate
t value given the area to the left of that t. Hence,
for a 95% confidence interval, we use .975. (Why .975? Because there's
0.025 to the right, and therefore 0.975 to the left.) As you should
recall from the reading, the degrees of freedom should be
t_star = qt(0.975, n-1)
Now, we're ready to compute the lower bound and upper bounds of the confidence interval using the standard formula.
ci_lower = x_bar - t_star*s/sqrt(n) ci_upper = x_bar + t_star*s/sqrt(n) c(ci_lower, ci_upper)
Of course, that's a lot of work. Hence, we might want to use the
t.test function, which provides not
just the confidence interval, but also a lot of other data. However,
we need to work from the original data set, rather than from the mean
and standard deviation already computed from that data set. (If you
only know mean, standard deviation, and sample size, you'll need to
use the technique above.) To use the
function, you also need to provide a hypothesized population
mu) and a desired confidence interval
conf.level). While you don't need mu to compute
the confidence interval, the t-test computes more
than just the confidence interval, and therefore requires a bit more.
t.test(BodyTemps$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)
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)
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