My table
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community
Ask the community for help and clear up your study doubts
University Rankings
Discover the best universities in your country according to Docsity users
Free resources
Our save-the-student-ebooks!
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Study Guide for Experiment Design and Analysis | PHYS 341, Exams of Physics
Material Type: Exam; Class: Design of Experiments; Subject: Physics; University: Christopher Newport University; Term: Unknown 1989;
Typology: Exams
2009/2010
1 / 2
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Study Guide for Experiment Design and Analysis | PHYS 341 and more Exams Physics in PDF only on Docsity!
My table
Test
Condition
Test Statistic
Tests of Hypothesis
Confidence Intervals
χ 2
χ
n 2 ( α )
σ 2 <
(n −
s 2
χ n 2 (α )
Single Variance
Normal Distribution
χ 2 =^
(n −
s 2
σ (^2)
χ 2 < χ^
n 2 ( (^) −
(^) α )
σ 2
(n −
s 2
χ n 2 ( − α )
χ n 2 ( 2 α (^) ) (^) < χ
2
χ^
n 2 ( (^) −
2 α (^) )
(n −
s 2
χ n 2 ( 2 α (^) )
< σ
2 <^
( n −
s 2
χ n 2 ( − 2 α (^) )
Normal Distributions
F > F
ν 1 ν 2 (^) ( α )
Two Variances
ν 1 (^) =
(^) n 1 (^) −
(^1)
F
s 12
s 22
F < F
ν 1 ν (^2) ( (^) −
(^) α )
ν 2 (^) =
(^) n 2 (^) −
(^1)
F
ν 1 ν 2 ( 2 α (^) ) (^) < F < F
ν 1 ν 2 (^) ( (^) −
2 α (^) )
z > z
α )
¯y < μ
0 (^) +
(^) z ( α ) √σ n
Single Mean
σ Known
z (^) =
¯y − μ 0
n√^ σ
z > z
(^) α )
¯y > μ
0 (^) −
(^) z ( α ) √σ n
z ( 2 α (^) ) (^) < z < z
2 α (^) )
¯y (^) =
(^) μ 0 (^) ±
(^) z ( 2 α (^) )
σ
√ n
t > t
n ( α )
¯y < μ
0 (^) +
(^) t n ( α ) s
√ n
Single Mean
σ Unknown
t (^) =
¯y − μ 0
s
√ n
t > t
n ( (^) −
(^) α )
¯y > μ
0 (^) −
(^) t n ( α ) s
√ n
t n ( 2 α (^) ) (^) < t < t
n ( (^) −
2 α (^) )
¯y (^) =
(^) μ 0 (^) ±
(^) t n ( 2 α (^) )
s
√ n
Independent Samples
z > z
α )
y 1 (^) −
(^) ¯y 2 ) (^) < z
α ) √
σ^ (^12)
n (^1)
σ (^22)
n 2
Two Means
σ (^12) (^) , σ
22 Known
z
¯y 1 − ¯y 2
√
σ^ (^12)
n (^1)
(^) σ 22
n 2
z > z
(^) α )
y 1 (^) −
(^) ¯y 2 ) (^) > z
(^) α ) √
σ^ 12
n 1
σ 22
n 2
z ( 2 α (^) ) (^) < z < z
2 α (^) )
y 1 (^) −
(^) ¯y 2 ) =
z ( 2 α (^) ) √
σ^ 12
n 1
(^) σ 22
n 2
Independent Samples
t > t
n 1 /n 2 (^) ( α )
y 1 (^) −
(^) ¯y 2 ) (^) < t
n 1 /n 2 (^) ( α ) √
(^ n 1 −
s 12 +( n 2 −
s 22
n 1
n 2 − 2
(
1 n^1
2 n^1 )
Two Means
σ (^1 ) , σ
(^22) Unknown,
t (^) =
¯y 1 − ¯y 2
√
(^ n 1 −
1 s 2 +( n 2 −
2 s 2
n 1
n 2 − 2
( n 1 1 (^) +
2 n^1 )
t > t
n 1 /n 2 (^) ( (^) −
(^) α )
y 1 (^) −
(^) ¯y 2 ) (^) > t
n 1 /n (^2) ( (^) −
(^) α ) √
(^ n 1 −
s 12 +( n 2 −
s 22
n 1
n 2 − 2
( n 1 1
2 n^1 )
but Equal
t n 1 /n 2 (^) ( 2 α (^) ) (^) < t < t
n 1 /n (^2) ( (^) −
2 α (^) )
y 1 (^) −
¯y 2 ) =
t n 1 /n (^2) ( 2 α (^) ) √
(^ n 1 −
s 12 +( n 2 −
s 22
n 1
n 2 − 2
(
1 n^1
2 n^1 )
Independent Samples
t > t
n dof
(^) ( α )
y 1 (^) −
(^) ¯y 2 ) (^) < t
n dof
(^) ( α ) √
s^ 12
n (^1)
s 22
n 2
Two Means
σ 12 (^) , σ
22 Unknown, Unequal
t (^) =
¯y 1 − ¯y 2
√
s^ 12
n (^1)
(^) s 22
n 2
t > t
n dof
(^) (
(^) −
(^) α )
y 1 (^) −
(^) ¯y 2 ) (^) > t
n dof
(^) (
(^) −
(^) α ) √
s^ 12
n 1
s 22
n 2
n dof
( s 12
n 1 (^) + (^) s 22
n (^2) )
(
1 n 1 s 2
n 1
(^) +
s 22
n 2
n 2
(^) ) − (^2)
t n dof
(^) ( 2 α (^) ) (^) < t < t
n dof
(^) (
(^) −
(^) α 2 (^) )
y 1 (^) −
(^) ¯y 2 ) =
t n dof
(^) ( 2 α (^) ) √
s^ 12
n (^1)
s 22
n 2
t < t
n ( α )
d < t¯
n ( α ) (^) s d
√ n
Two Means
Correlated Samples
t (^) =
d^ sd¯
√ n
t > t
n ( (^) −
(^) α )
d > t¯
n ( (^) −
(^) α ) (^) s d
√ n
d (^) =
(^) y 1 (^) −
(^) y 2
t n ( 2 α (^) ) (^) < t < t
n ( (^) −
2 α (^) )
d¯ (^) =
(^) ±
t n ( 2 α (^) ) (^) s d
√ n