This example uses the speeds on Triphammer Road from De Veaux, Velleman
and Bock, *Stats.: Data and Models* 2nd ed., 2008, Addison Wesley,
Boston. (It's the first example in Chapter 23.) Police measured traffic
speeds (in miles per hour) on a road where this was a concern. Here are
the results.

29 34 34 28 30 29 38 31 29 34 32 31 27 37 29 26 24 34 36 31 34 36 21

The R `scan` function allows you to enter data without typing
commas. In the case below, the values were not actually typed but inserted
with cut and paste. The "24:" prompt means R has received 23
numbers and is waiting for the 24^{th}. Hit RETURN to cease data
entry.

> speeds = scan() 1: 29 34 34 28 30 29 38 31 29 34 32 31 27 37 29 26 24 34 36 31 34 36 21 24: Read 23 items > stem(speeds) The decimal point is 1 digit(s) to the right of the | 2 | 14 2 | 6789999 3 | 0111244444 3 | 6678 > stem(speeds, scale=2) The decimal point is at the | 20 | 0 22 | 24 | 0 26 | 00 28 | 00000 30 | 0000 32 | 0 34 | 00000 36 | 000 38 | 0 > summary(speeds) Min. 1st Qu. Median Mean 3rd Qu. Max. 21.00 29.00 31.00 31.04 34.00 38.00 > t.test(speeds, mu=30, alternative="greater", conf.level=0.90) One Sample t-test data: speeds t = 1.1781, df = 22, p-value = 0.1257 alternative hypothesis: true mean is greater than 30 90 percent confidence interval: 29.87323 Inf sample estimates: mean of x 31.04348

Note that a single command returns both a hypothesis test and a
confidence interval and that one-sided tests return one-sided confidence
intervals (as they should). The confidence level must be specified as a
number between 0 and 1. Another alternative for `alternative` is "less".
Leaving it out gives a two-sided test/interval. The default mu is 0 and
the default confidence level 95%=0.95. In the textbook example, the
question was whether the average speed exceeded 30 miles per hour so
that's what we tested. We could question the result on two grounds. First,
the stem and leaf shows the data bimodal and skewed toward low values (or
is that an outlier?), and checking the mean may not be the appropriate
tool here. Second, even though the average speed was close to 30, we can
note that a majority of the vehicles were exceeding the 30 MPH speed
limit.

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