The document discusses statistical hypothesis testing, including concepts like population proportions, critical values, and types of errors. It outlines the methods for conducting tests such as lower tail, upper tail, and two-tailed tests, specifying criteria for rejecting null hypotheses. Additionally, it emphasizes the importance of standard errors, confidence intervals, and central limit theorem when dealing with sample data.

1. -
population ( parameters M ) -
( l -
a) is confidence level
+ =
⇒
-
finite ( N )
-
PC tzta ,✓)=F Str
~tn -1
-
simple random sample [ I -
ten 'Fn ,I+tE,v
.
In ] 4. Determine crit .
value
( same prob .
of being selected ) -
When n > 1000 ,
Use Standard -
lowertailtestcha :m< Mo ) :P( ztzxta
-
infinite normal Table -
uppertailtestltta :M > Mo ) :P( 2 > Zxkx
-
random sample ( each elm .
2. population proportion twotailtestltta :m¥mo )
Comes from same pop . E. is
-
( 1 -
X ) is Confidence level
-
lfteststatoo :P( 2<-2 ; )=E
selected independently ) [ F- 2
;
F
"n⇒
'
, 15+2;
F
"n→
'
] -
ifteststat > o :p( z >
zq)=E
-
pop . mean : M .
desirable
margin
of error 5. Compare Critval . { test . Stat
-
pop .
Std :O
-
pop .
mean WIO known towertailtest :
lfteststattzxirejecttto
-
pop .
proportion :p
-
Zxz
Fntmarginoferrr -
upper tail test :# teststat > zx :
reject Ho
.
Sample ↳ solve n
-
twotailtest :
-
point estimator
-
pop .
prop .
-
Ifteststatcoteststattzairejecttto
-
sample Mean :I -
2g
#nt= margin of error
-
ifteststat > oteststat >
zq
:
reject Ho
-
sample Std :S 3. difference in means
type terror :
reject Ho when
-
sample proportion :p
-
A=I ,
-
Iz Hoistrul
-
Underlying pop has expected
-
E 1 d) =M ,
-
Mz
type # error :
accept Ho
value ME variance 02 -
Varcd )=¥+ ⇒ when Ho is false
-
ELI )=M -
a~N( M ,
-
Mz ,
# +
¥ ) .
level ofsig ( × ) :
maxprob .
02
-
Vara )=T a) O , ,Oz known that can be tolerated for
-
Stdlx )= TF =0E
[ ixixz ,
.ee#Font.uixz)+qfEn.+nEztftypeIerr0r
↳ standard error of mean
.
p
-
value approach ( Gknown )
-
I~N( M ,
# ) if pop .
b) 0 , ,0z Unknown 1. Develop Ho ,
Ha
is normally distributed or
→
assume 0 ,=oz=op 2. Specify ×
if n >_ 30 ( central limit theorem
)Var(4) =Op2(÷ntn÷ ) 3. Cakteststat Z*
-
EC f)
=÷E(
xktnlnp )=p .
Pooled sample variance 4. Computers -
value
-
Var( F) = ( ht )2Var( × ) -
sp2=
5 ? ( ni -
1) +5221^2-1 ) -
lowertailtest :p .
vai .=p(z<z* )
=
ntznp ( 1 -
D) = #fe= 0,52 Ni +
nz
-
2 -
upper tail test :p -val=p( 2>2*1
-
Std (f) =
0,5=5*3
' -
Var (d) ~~Sp2( F. +
th ) -
ztail : if 2*0 ,p-vai=zp(2<z* )
↳ standard error
-
Std (d) =
Sptnfhz ifz*>o ,p-vai=zp( 2>2*1
-
F~N( p ,
#n# ) When -
Uset -
distribution 5. Compare p-valGx
npzg { n( 1 -
p )z5 [hiixzttezirspfnttnz .LI#zlttE.vsPFnntz ] -
If pval > x. cannot reject Ho
.
Interval Estimation
-
V=n,+nz -
2 -
lfp .
vak x. reject Ho
1.
pop .
mean M
.
hypothesis testing pop .
prop .
-
teststat :Z*= F -
P
a) oknown
-
Critical value approach repos
-
( l -
X ) is Confidence ( Usedfcroknownoq
-
Canusecritval .
orpval .
difference in means
level UNKNOWN ) -
easel :O , Gozknown
-
PL -
BEZE b) =1 -
X 1. Develop Ho ,
Ha Teststat :z*=I .
-
Ez -
do
IOI -
b) =F 2. Specify levelofsigx
It #
PCZ > ZE )= E 3. cake . test Stat
-
Case 2 :O ,
EQ unknown
-
Assume 01=02
[ I -2g
.
In ,I+Zq
.
# ] Z for 0 known
tes+s+a+:t*=
I # 2- do
b) 0 Unknown I -
Mo SP in
,
+
's
Ztoyn ~N( Oil ) *
useomycritval . approach-
t distribution
degrelsoffreedomfort : n ,
+
nz
-
2
-
degrees of freedom =V=n -
Itfor 0 unknown