Download Estimate, Std Err, Confidence Interval, Hypothesis

STAT 3000
Getting a Point Estimate, Standard Error, and t-Interval for a
Single Population Mean from SAS
This is a continuation of the metal cylinder data discussed in Example 14 of the textbook (see pages 268, 273, 285,
330, 333, 346, 351, and 361), and discussed in the previous handout titled “Using SAS Software and Obtaining
the Datasets Used in the Text”. The program below reads in these data (stored in the file
fig6.5-metal-cylinders.txt), computes the mean and standard error of the mean, constructs a two-sided
confidence interval for average diameter (see page 330), and computes a test statistic and p-value for a test of the
null hypothesis that the average diameter is equal to 50 mm (see pages 346, 351, and 361).
data cylinder;
infile "C:\CHRIS\CLASSES\STAT3000\datasets_third_ed\ASCII tabbed datasets\Chapter
6\fig6.5-metal-cylinders.txt" firstobs=2;
input diameter;
run;
proc means data=cylinder;
var diameter;
run;
proc ttest data=cylinder h0=50;
var diameter;
run;
proc ttest data=cylinder h0=50 alpha=0.01;
var diameter;
run;
PROC MEANS is a quick way of getting a few basic summary statistics (unlike the volume of output produced by
PROC UNIVARIATE), including the sample mean and standard deviation.
PROC TTEST allows you to obtain a confidence interval and p-value for a hypothesis test. The output from this
proc also includes the standard error of the sample mean. Note that for this example we are interested in whether
the machine is calibrated incorrectly – correct calibration in this case is manifested by an average diameter of 50
mm. The “null hypothesis” therefore is that the average is 50, versus the alternative that it is not 50. This
hypothesis is specified by the h0=50 option in the PROC TTEST statement.
One last note: the default value for alpha is 0.05, although you can specify any value you wish using the alpha=
option, as shown above. As an illustration, the second PROC TTEST uses and alpha of 0.01, which yields a 99%
confidence interval.
The raw output is shown on the page following, but in summary we conclude that the average metal diameter for
this machine is 49.999, with a standard deviation of 0.1337 and a standard error of 0.0173. We are 95% confident
that the average diameter for this machine is between 49.9643 and 50.0334 mm. (And 99% confident that the
average diameter is between 49.9529 and 50.0448 mm.) To test that the machine is calibrated correctly, with an
average diameter of 50 mm, SAS reports a t statistic of -0.07 (on 59 df), with a p-value of 0.95. There is no
evidence whatsoever that the machine is incorrectly calibrated.
RAW OUTPUT
PROC MEANS:
Analysis Variable : diameter
N
Mean
Std Dev
Minimum
Maximum
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60
49.9988333
0.1336968
49.7400017
50.3600006
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FIRST PROC TTEST:
The TTEST Procedure
Variable:
diameter
N
Mean
Std Dev
Std Err
Minimum
Maximum
60
49.9988
0.1337
0.0173
49.7400
50.3600
Mean
49.9988
95% CL Mean
49.9643
Std Dev
50.0334
95% CL Std Dev
0.1337
0.1133
DF
t Value
Pr > |t|
59
-0.07
0.9463
0.1631
SECOND PROC TTEST:
The TTEST Procedure
Variable:
N
Mean
Std Dev
Std Err
Minimum
Maximum
60
49.9988
0.1337
0.0173
49.7400
50.3600
Mean
49.9988
.
diameter
99% CL Mean
49.9529
Std Dev
50.0448
0.1337
DF
t Value
Pr > |t|
59
-0.07
0.9463
99% CL Std Dev
0.1078
0.1742