Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
A 95 percent confidence <strong>in</strong>terval for µ<br />
<strong>Overview</strong> <strong>of</strong><br />
<strong>basic</strong> <strong>concepts</strong><br />
<strong>in</strong> <strong>Statistics</strong><br />
<strong>and</strong><br />
<strong>Probability</strong><br />
Avanti<br />
Athreya<br />
Prelim<strong>in</strong>aries<br />
Important<br />
distributions,<br />
scal<strong>in</strong>g laws,<br />
<strong>and</strong> the CLT<br />
Parametric<br />
estimation <strong>and</strong><br />
hypothesis<br />
test<strong>in</strong>g<br />
So we know<br />
P<br />
(<br />
Thus<br />
(∑ n<br />
1<br />
P<br />
X i<br />
n<br />
−1.96 <<br />
∑ n<br />
1 X )<br />
i<br />
n<br />
− µ<br />
σ/ √ < 1.96 = .95<br />
n<br />
− 1.96σ √ n<br />
< µ < 1.96σ √ n<br />
+<br />
<strong>and</strong> the r<strong>and</strong>om <strong>in</strong>terval<br />
(∑ n<br />
1 X i<br />
− 1.96σ ∑ n<br />
√<br />
1<br />
,<br />
X i<br />
n n n<br />
∑ n<br />
1 X )<br />
i<br />
= 0.95<br />
n<br />
+ 1.96σ )<br />
√ n<br />
is called a 95 percent confidence <strong>in</strong>terval for µ.<br />
In a large number <strong>of</strong> draws <strong>of</strong> the r<strong>and</strong>om sample, this <strong>in</strong>terval<br />
will conta<strong>in</strong> the true value µ about 95 out <strong>of</strong> 100 times.
Change language