This file was generated by AnalyzeEverything (www.norrsken-data-teknik.com)

The Original Data Tables:

The Analyzing Results:

The Chi-Square Test

The data distribution Σ Anzahl = f ( Note ) has been tested against the binomial distribution with the parameters
n_{max. class index}=18
p₀=0.1844
sum_{Σ Anzahl}=50.0

(This has been calculated by the parameters
mean-arg_Note=4.32
standard-deviation_Note=1.6424)

The chi-square test with the
significance level 0.95
(error probability 5.0%)
and the degree of freedom m = n -1
(manually changed the number of classes, class borders)
m_Note = 5
(reduced by 2 because the mean-value and the standard-deviation are unknown and hence calculated)
produces the chi-square values
chi²_{Σ Anzahl} = 34.291
chi²_{0.05, 3} = 0.37.

If the condition
chi²_{Σ Anzahl} < chi²_{0.05, 3}
is true, the assumption that the distribution is binomial can be accepted.

So the theory, Note is randomly distributed, must be rejected.

The data distribution is

The Chi-Square Test

The data distribution Σ Anzahl = f ( Note ) has been tested against the binomial distribution with the parameters
n_{max. class index}=18
p₀=0.1844
sum_{Σ Anzahl}=50.0

(This has been calculated by the parameters
mean-arg_Note=4.32
standard-deviation_Note=1.6424)

The assumption is now: The data is not randomly distributed.

The chi-square test with the
significance level 0.95
(error probability 5.0%)
and the degree of freedom m = n -1
(manually changed the number of classes, class borders)
m_Note = 5
(reduced by 2 because the mean-value and the standard-deviation are unknown and hence calculated)
produces the chi-square values
chi²_{Σ Anzahl} = 34.291
chi²_{0.95, 3} = 7.82.

If the condition
chi²_{0.95, 3} < chi²_{Σ Anzahl}
is true, the assumption that the distribution is not binomial can be accepted.

So the theory, Note is not randomly distributed, can be accepted.

The data distribution is

The STUDENT t-test

The data distribution Σ Anzahl = f ( Note ) has been tested against the binomial distribution with the parameters
n_{max. class index}=18
p₀=0.1844
sum_{Σ Anzahl}=50.0

(This has been calculated by the parameters
mean-arg_Note=4.32
standard-deviation_Note=1.6424)

The STUDENT t-test with the
significance level 0.95
(error probability 5.0%)
and the degree of freedom m = n -1
(manually changed the number of classes, class borders)
m_Note = 5
produces the t-test values
T_{Σ Anzahl} = 76.677
t_{0.95, 5} = 2.59.

If the condition
T_{Σ Anzahl} < t _{0.95, 5}
is true, the assumption that the distribution is binomial can be accepted.

So the theory, Note is randomly distributed, must be rejected.

The data distribution is