ORM.S.INV(α) (z-score should be negative)
ORM.S.INV(1-α) (z-score should be positive)
.INV(α,df) (t-score should be negative)
.INV(1-α,df) (t-score should be positive)
Two-tailed tests: z
α/2
= NORM.S.INV(α/2) (both the + and – are critical)
Two-tailed tests: t
α/2
= T.INV(α/a,df) ((both the + and – are critical)

Formula for the z-Test statistic
for a Hypothesis Test for the
proportion
(zp)
Upper-tailed test: reject H
0
when test statistic (z
xbar
, t
xbar
, or z
p
) > critical test statistic (z
α
o
Lower –tailed test: reject H
0
when test statistic (z
xbar
, t
xbar
, or z
p
) < critical test statistic (z
α
Upper-tailed test: reject H
0
when test statistic (z
xbar
, t
xbar
, or z
p
) < OR > critical test statisti
H
0
n
p
p
p
p
z
H
H
H
p
)
1
(
0
0
0

Two tailed
Test (insert the
symbols)
Two tailed, Upper
Tailed, or Lower
Tailed?
Ho: u
=
56
This test would be used by someone that wants to
prove that the average is __
different
than 56.
H1: u
/=
56
Ho: u
<=
56
Upper ; alternative
hypothesis has >
symbol.
This test would be used by someone that wants to
prove that the average is ___
higher
_ than 56.
H1: u
>
56
Ho: u
>=
56
Lower ; alternative
hypothesis has <
symbol.
This test would be used by someone that wants to
prove that the average is _
less
____ than 56.
H1: u
<
56

or t
α
)
α
or t
α
)
tic (z
α/2
or t
α/2
)

Rules
what we want to prove goes in the alternative
the equals always goes in the null
1
<=
0.7
the proportion of people who plants to be E-filers for t
>
0.7
is greater than 70%
Test:
One tail Upper
2
=
2.9
must divided
Alpha/2
to get upper and lower -zCri
/=
2.9
so the average #of tv's in the home of consumers com
Test:
Two Tail Test
3
>=
60
<
60
Test:
One tail Lower
critical zscore should be negative.
the current average time on the market is less than 60 days.
H
0
H
1
H
0
H
1
H
0
H
1

the next tax season
itical & Zscore
mcast is not 2.9
One-Tailed Test: Find z-score at __
α
_______ in the tail
Two-Tailed Test: Find z-score with _
α
/2
______ in the tail

type of test:
n=
std dev=
u=
a=alpha
type of test:
n=
u=
std dev=
a=
type of test:
n=
u=
std dev=
a=
H
0
H
1
H
0
H
1
H
0
H
1

u
<=
40
u
>
40
one tail upper
the average age of customers is greater than 40 yrs old.
60
8
42.7
0.02
u
=
5
u
/=
5
Two tail test
ZINCO'S CUSTOMERS DOESNOT SPEND FIVE MINUETS FOR SERVICE.
45
5.5
1.7
0.02
u
>=
20
u
<
20
one tail lower
THE AVERAGE WAIT TIME FOR TABLE IS LESS THAN 20 MIN.
45
18.3
5
0.05

Step 1
Identify the Null and Alternative Hypothesis
u
>=
20
u
<
20
type of test:
type of test:
one tail lower
THE AVERAGE WAIT TIME FOR TABLE IS LESS THAN 20
Step 2
alpha
α
0.05
Step 3
Determine the appropriate critical z-score
z at alpha
NORM.S.INV(ALPHA)
-1.644854
-1.645
Step 4
Calculate the appropriate test statistic (test zscore)
n
45
xbar
18.3
pop std dev
5
numerator
-1.7 xbar - uHo
denominator
0.745355992 std error
test zscore
-2.28078934
Step 5
Compare Test Zscore againts Critical Zscore
test zscore
critical zscore
-2.28078934 <
-1.644853627
Step 6
State your conclusions
H
0
H
1
Set a value for the significance level, α
n
σ
μ
x
z
H
x
0

we reject the Null and conclude in the Alternative that,
THE AVERAGE WAIT TIME FOR TABLE IS LESS THAN 20 MIN.

STP1
u
>=
20
u
<
20
type of test:
one tail lower
THE AVERAGE WAIT TIME FOR TABLE IS LESS THAN 20 MIN.

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- Spring '15
- Null hypothesis, Statistical hypothesis testing, Critical Zscore, test zscore