Introduction to Statistics (MAT/SST 115.03 2008S)
You can load the sample NBA points data with
nba = read.csv("/home/rebelsky/Stats115/Data/NBAPoints.csv")
You will note that there are two columns in the data frame: One for the date in which the game was played and one for the total score that night.
1 12/10/1999 196
2 12/10/1999 198
3 12/10/1999 205
4 12/10/1999 163
5 12/10/1999 184
6 12/10/1999 224
It's been awhile, so you may not remember the techniques we use for visual displays of quantitative data. Let's review. You can try
library(BHH2, lib="/home/rebelsky/Stats115/Packages") dotPlot(nba$Points)
qqnorm(nba$Points, datax=T) qqline(nba$Points, datax=T)
A quick reminder ...
You should compute the t-test statistic using the formula on p. 395. Note that you'll need to parenthesize the denominator.
(x_bar - mu_0)/(s/sqrt(n))
After using the applet, you might also just want to have R compute the test statistic and p-value directly from the original data.
t.test(nba$Points, mu=183.2, alternative="greater")
Sometimes you just have the test statistic, and not the original data
(or just the mean and standard deviation, and not the original data,
in which case you can compute the test statistic). In that case,
you can still have R compute the p-value using
pt function. You need to supply the test
statistic and the degrees of freedom. As is the case for the
standard normal probability table, this gives the area to the
left, so you will need to subtract it from 1.
We will need two data sets for this activity, a set of sleep times for
this class (
SleepData.csv) and a set of hypothesized sleep
HypoSleep.csv). Let's start with our class.
classdata = read.csv("/home/rebelsky/Stats115/Data/SleepData.csv")
So, what does that table look like again?
Okay, just one column, named
HoursSlept. How many values
are in that column?
What about the hypothetical data?
hyposleep = read.csv("/home/rebelsky/Stats115/Data/HypoSleep.csv")
And what are those columns named?
Sample1 Sample2 Sample3 Sample4
1 7.5 5.1 6.1 7.7
2 7.4 9.1 7.3 8.4
3 6.8 4.7 6.1 5.6
4 7.3 5.2 6.9 5.0
5 6.1 7.2 6.5 5.9
6 5.4 5.3 5.2 8.9
The authors clearly intend for you to do this test “manually”, first computing the mean and standard deviation, then computing the test statistic, and finally looking up the p-value in the table.
There are two kinds of technology appropriate for filling in the table. You can use the applet. I'll admit that I find that an attractive option, since it shows you the parts of the curve for that proportion.
However, you may find it easier, faster, and more accurate to use R. Minimally, you should know what commands are appropriate. In this case, our alternative is two-sided, so we use a slightly different command.
t.test(hyposleep$Sample1, mu=7, alternative="two.sided") t.test(hyposleep$Sample2, mu=7, alternative="two.sided") t.test(hyposleep$Sample3, mu=7, alternative="two.sided") t.test(hyposleep$Sample4, mu=7, alternative="two.sided")
You can read the data with
br = read.csv("/home/rebelsky/Stats115/Data/BeadedRectangles.csv")
Since you do not have the original data, you cannot use the helpful
t.test function. Instead, you will need to
compute the test statistic manually and then use
to find the p-value.
Of course, you can also use the applet.
Copyright (c) 2007-8 Samuel A. Rebelsky.
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