Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Sufficient statistic wikipedia , lookup

Bootstrapping (statistics) wikipedia , lookup

Foundations of statistics wikipedia , lookup

Psychometrics wikipedia , lookup

Taylor's law wikipedia , lookup

Omnibus test wikipedia , lookup

Misuse of statistics wikipedia , lookup

Resampling (statistics) wikipedia , lookup

Student's t-test wikipedia , lookup

Transcript
Problem Identification:
Hypothesis Test of the Variance using the Chi-Square Distribution
Fill in the Yellow areas. The green areas will be automatically updated based on your inputs.
1. The population parameter of interest is the mean (describe the application)
Describe the parameter here
2. The Null Hypothesis makes this claim about the population Variance:
σ2
(sigma,
<=
0.0004
units
squared)
↑↑↑
↑↑↑ ↑units of measure
(put <= or = or >= in this box)
(put a number value in this box)
(use '= to get Excel to accept =)
ok
ok
3. The Alternative Hypothesis makes this claim about the population Mean:
σ2
>
0.0004
units
5. We are using the Chi-Square Distribution
We are assuming that the population is generally normally distributed.
6. We choose the level of significance for this test to be
(alpha)
α
=
0.05
ok
This is a one-tailed
test.
on the
right side
The Alternative Hypothesis occupies probability of
0.0500
(5%)
in the right tail
7. We have collected sample data from the population:
The sample variance is:
s2
=
0.0007
and the sample size is:
n
=
28
therefore the degrees of freedom is:
df = n - 1
=
27
ok
All Inputs Ok?
= TRUE
ok
8. The calculated value of the Test Statistic is
χ2
=
47.2500 =(df*SampleVariance)/(NullHypothesisValue)
Area to the left of this is:
0.990701
(n  1)  s 2
Area to the right of this is:
0.009299
 2* 
2

9. p-Value approach:
The probability that the Test Statistic
is this value, or more extremely,
TestStat
>
47.2500 , is
pValue: 0.009299
<=
0.05
and this pValue is
LESS THAN α
or 9. Critical Value approach
The Critical Value is =CHIINV(alpha or alpha/2, df)
40.1133
The Test Statistic,
47.2500
is INSIDE the Critical Region.
Excel formulas for critical values:
=CHIINV(IF(Tailed="one-tailed",alpha,alpha/2),df)
p-Value formula:
=IF(Tailed="two-tailed",CHIINV(1-alpha/2,df),"")
=IF(Tail="left",1-CHIDIST(TestStatistic,df),CHIDIST(TestStatistic,df))
10. Conclusion:
REJECT
There IS sufficient evidence at the α = 0.05 level of significance
to reject the null hypothesis.
Problem Identification:
Hypothesis Test of the Variance using the Chi-Square Distribution
Fill in the Yellow areas. The green areas will be automatically updated based on your inputs.
1. The population parameter of interest is the mean (describe the application)
Describe the parameter here
2. The Null Hypothesis makes this claim about the population Variance:
σ2
(sigma,
squared)
↑↑↑
↑↑↑ ↑units of measure
(put <= or = or >= in this box)
(put a number value in this box)
3. The Alternative Hypothesis makes this claim about the population Mean:
σ2
5. We are using the Chi-Square Distribution
We are assuming that the population is generally normally distributed.
6. We choose the level of significance for this test to be
(alpha)
α
=
This is a
test.
The Alternative Hypothesis occupies probability of
7. We have collected sample data from the population:
The sample variance is:
2
s
=
and the sample size is:
n
=
therefore the degrees of freedom is:
df = n - 1
=
8. The calculated value of the Test Statistic is
2
χ
=
Area to the left of this is:
Area to the right of this is:
9. p-Value approach:
The probability that the Test Statistic
is this value, or more extremely,
TestStat
, is
pValue:
and this pValue is
10. Conclusion:
 2* 
(n  1)  s 2
2
or 9. Critical Value approach
The Critical Value is =CHIINV(alpha or alpha/2, df)
The Test Statistic,
is
There seems to be no built-in Excel function.
Use formulas like the "Automatic" sheet to
accomplish this kind of a test.
There is the Analysis add-in's "F-Test Two-Sample
for Variances".
There seems to be no built-in STATS > TEST feature
for this kind of a problem.
≠
Related documents