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Chapter 9.1 Notes.docx-Hypothesis Tesng...
Chapter_9.1_Notes.docx-Hypothesis Tesng For Populaon Mean 1)
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California_State_University-Fullerton
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Business_Analytics_I_3
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Chapter 9.1 Notes.docx
Chapter_9.1_Notes.docx
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Chapter 9.1 Notes.docx-Hypothesis Tesng For Popul...
Chapter_9.1_Notes.docx-Hypothesis Tesng For Populaon Mean 1)
Chapter 9.1 Notes.docx-Hypothesis T...
Chapter_9.1_Notes.docx-Hypothesis Tesng For Populaon Mean 1)
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Page 1
Hypothesis Tesng For Populaon Mean
1) Determine the alternave hypothesis
a.
Check the problem for key words; the alternave hypothesis will never
contain an equal sign
i. H
a
: µ < µ
o
1.
“develop appropriate hypothesis for a test to determine
whether sample data supports the conclusion that the mean
cost is less than / has decreased…”
ii. H
a
: µ > µ
o
1.
“develop appropriate hypothesis for a test to determine
whether sample data supports the conclusion that the mean
cost is more than / has increased…”
iii. H
a
: µ ≠ µ
o
1.
“state the hypothesis that can be used to test whether the
mean differs from…”
2) Determine the null hypothesis
a.
The null hypothesis will always be the opposite of the alternave
hypothesis; will always contain an equal sign
i.
If H
a
: µ < µ
o
1.
Then H
o
: µ ≥ µ
o
ii.
If H
a
: µ > µ
o
1.
Then H
o
: µ ≤ µ
o
iii.
If H
a
: µ ≠ µ
o
1.
Then H
o
: µ = µ
o
3) Determine which tail test to use
a.
Look at the alternave hypothesis to assess which tail
i.
If H
a
: µ < µ
o
and H
o
: µ ≥ µ
o
1.
Then Leſt/Lower-Tailed Test
ii.
If H
a
: µ > µ
o
and H
o
: µ ≤ µ
o
1.
Then Right/Upper-Tailed Test
iii.
If H
a
: µ ≠ µ
o
and H
o
: µ = µ
o
1.
Then Two-Tailed Test
Page 2
4) Record all necessary informaon from the problem
a.
Hypothesized Value of Populaon Mean (µ
o
)
i.
This is the numerical value used in your null hypothesis
b.
Sample Mean (x̅)
c.
Sample Standard Deviaon (s) or Populaon Standard Deviaon (
σ
¿
i.
Make sure to label these properly; it makes a difference later
d.
Sample size (n)
e.
Level of significance (α)
5) Find the Standard Error of x̅
a.
If you are given the Populaon Standard Deviaon (
σ
¿
i.
Then σ
x̅
=
σ
√
n
b.
If you are given the Sample Standard Deviaon (s)
i.
Then s
x̅
=
s
√
n
6) Find the Test Stasc
a.
z =
x
−
µo
σ
√
n
=
x
−
µo
σ x̅
i.
Recall the cell in step five for the Standard Error of x̅
7) Find the P-Value based on which tail the test is
a.
If you are given the Populaon Standard Deviaon (
σ
¿
i.
If Leſt/Lower-Tailed Test
1.
Then =NORM.S.DIST(test stasc, TRUE)
a.
Recall the cell in step six for Test Stasc
ii.
If Right/Upper-Tailed Test
1.
Then =1-NORM.S.DIST(test stasc, TRUE)
a.
Recall the cell in step six for Test Stasc
iii.
If Two-Tailed Test; determine which formula to use based on if the
test stasc is negave or posive
1.
If Test Stasc is Negave
a.
Then = 2*NORM.S.DIST(test stasc, TRUE)
2.
If Test Stasc is Posive
a.
Then = 2*(1-NORM.S.DIST(test stasc, TRUE))
Page 3
b.
If you are given the Sample Standard Deviaon (s)
i.
If Leſt/Lower-Tailed Test
1.
Then =T.DIST(test stasc, n-1, TRUE)
a.
Recall the cell in step six for Test Stasc
ii.
If Right/Upper-Tailed Test
1.
Then =1-T.DIST(test stasc, n-1, TRUE)
a.
Recall the cell in step six for Test Stasc
iii.
If Two-Tailed Test; determine which formula to use based on if the
test stasc is negave or posive
1.
If Test Stasc is Negave
a.
Then = 2*T.DIST(test stasc, n-1, TRUE)
2.
If Test Stasc is Posive
a.
Then = 2*(1-T.DIST(test stasc, n-1, TRUE))
8) Assess the P-Value compared to the Level of Significance
a.
If P-Value ≤ α
i.
Then Reject H
o
1.
Significant evidence to support the alternave hypothesis
b.
If P-Value > α
i.
Then Fail to Reject H
o
1.
Do not say “Accept H
a
” as it could cause a Type II Error
2.
Not enough evidence to support the alternave hypothesis
9) Find the Crical Value
a.
If you are given the Populaon Standard Deviaon (σ)
i.
If Leſt/Lower-Tailed Test
1.
Then =NORM.S.INV(α)
ii.
If Right/Upper-Tailed Test
1.
Then =NORM.S.INV(1-α)
iii.
If Two-Tailed Test
1.
Then =NORM.S.INV(α/2)
a.
Negave Crical Value
2.
Then =-NORM.S.INV(α/2)
a.
Posive Crical Value
b.
If you are given the Sample Standard Deviaon (s)
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