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as car %2 MrAb“ Example: Cholesterol levels. The cholesterol levels of a control group were
measured and it was
found that the mean level was 193. Levels on 28 heart attack patients 2 days after the attack were measured:
270 236 210 142 280 272 160 220 226 242 186 266 206 318 294
282 234 224 276 282 360 310 280 278 288 288 244 236 Question: Is the mean of this group different
from 193? (Probably) First issue: How normal is the data? Frequency Histogram of chol 12 10 N 
O  100 150 200 250 chd 300 350 400 Normal QQ Plot Sample Quantiles
200 250 300 350 150 Theoretical Quantiles > t.test(chol,aIternative="two.sided",mu=1 93)
One Sample ttest data: chol t = 6.7575, df = 27, pvalue = 2.953e07
95 percent CI: [235.4284, 272.4288]
sample estimates: mean of x: 253.9286 36’. 7 Default confidence level is .95 but easy to
change:
t.test(chol,alternative="two.sided",mu=193,
conf.level=.99) One Sample ttest data: chol t = 6.7575, df = 27, pvalue = 2.953e07
99 percent confidence interval:
[228.9469, 278.9103] Note: If you want to be more confident (alpha=.1,
1alpha=.99) you get a wider interval. Op NoOp
2.6 1.2
2.0 1.8
1.7 1.8
2.7 2.3
2.5 1.3
2.6 3.0
2.5 2.2
3.0 1.3
1.5
1.6
1.3
1.5
2.7
2.0 3637 Example: Parkinson’s Among other things Parkinson’s
disease affects the ability to
speak. In a study on Parkinson’s,
eight of the afficted people
received a common operation to treat the disease.
This procedure seems to
improve overall condition but
does it improve ability to speak?
Patients were given several tests to measure
problems with speaking and the
higher the score, the more
problems with speaking. Results
are summarized below where “Op=operation” and
“NoOp=no operation performed”. The NoOp numbers leave us with a feeling of
more small values so it is not clear the operation
has a beneficial effect. We make a CI on
differences of means to test for the significant difference. t.test(op,noop,alternative="two.sided",mu=0)
data: op and noop t = 3.025, pvalue = 0.007132 95 percent confidence interval: [0.1927797, 1.0643632] sample estimates: mean of x mean of y
2.450000 1.821429 Remarks:  The 95% CI for mu_op —mu_noop is [0.19,
1.06] and with 95% confidence one believes
that mu_op>mu_noop. ° The means are not equal and there is a
definite difference between the 2
populations of op and noop. The noOP patients have better scores for speaking
ability. ...
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 '08
 WEBER

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