Download - Formula Sheet Non-cumulative Final F2011
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Final Exam, BU/EC255, Fall 2011
Formulae and Statistical Tables Booklet
Non-Cumulative Version
INSTRUCTIONS
1. Nothing may be written on or in this formula booklet, other than your name and
number.
2. Any student found with anything written on or in the formula booklet during a test or
exam will have the entire booklet confiscated.
3. Additionally, students may be subject to proceedings under the university's
regulations on academic honesty.
4. Students must use their own booklet
Name:
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Inference about One Population
CI of when is known
nzx 2 /
CI of when is unknown
1, / 2n
s x t
n
CI of p
/ 2 (1 ) / p z p p n
Sample size to estimate when is known
2
/ 2 zn E
= ; If is unknown, approximate using Range/4.
Sample size to estimate p
2 / 2
2
(1 ) p p zn
E =
Test statistic for testing when is known
/
x z
n
=
Test statistic for testing when is unknown
Test statistic for testing p
1n
xt
s n
=
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Inference about Two Populations
z-test of 1111 2222 when population variances are known:
( ) ( )1 2 1 22 2
1 2
1 2
x x z
n n
=
+
CI of 1 2: known variances
( )2 2
1 21 2
1 2 / 2 z x x n n
+
t-test of 1111 2222 when population variances are unknown but equal:
1 2 2n nt + =
( ) ( )1 2 1 2
1 2
1 1 p
x x
sn n
+,
( ) ( )
2nn
s1ns1ns
21
222
2112
p
+
+=
CI of 1 2: unknown but equal variances
1 21 2 2, / 2
1 2
1 1( ) *n n p x x t s n n +
+
t-Test of D
1 /
n
d
d Dt
s n
=
CI of D
1, / 2d
n
sd t
n
T f
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CI of p 1 p 2
( )2
22
1
112 / 21 n
)p1(pn
)p1(pzpp +
One-Way ANOVA Table
2
1
( )C
i ii
SSC n x x=
=
2
1( 1)
C
i ii
SSE n s=
=
Simple (k=1) and Multiple (k 2) Regression Analysis
Standard Error of Estimate
2eSSE
Sn
=
Coefficient of determination
2
YY
SSR RSS
=
Adjusted 2 R :
2 2 /( 1) 11 1 (1 )/( 1) 1 A
SSE n k n R R
SS n n k
= =
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ANOVA Table
Testing the Slope Coefficient i
1
i
i in k
b
bt
s
=
CI ofi
/2, 1* ii n k bb t s
For Simple Regression Analysis ONLY
Confidence Interval for average Y:
( )20 / 2, 2
1 * *SSn e xx
X X Y t S
n
+
Prediction Interval for individual Y:
( )20 / 2, 2
1 * * 1SSn e xx
X X Y t S
n
+ +
Test Statistic for Chi-squared tests:
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Table A.5 Areas of the Standard Normal Distribution
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Table A.6 critical Values from the t Distribution
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Table Chi-squared Distribution