1. The document outlines various statistical tests and their associated formulas, degrees of freedom, and levels of significance. 2. Tests discussed include chi-square test for goodness of fit, test for independence of attributes, t-test for single mean, test for difference of means, paired t-test, F-test for variance, Z-test for single mean/difference of means/proportion, and run test. 3. For each test, the document provides the formula used, degrees of freedom, which depends on factors like the number of samples or attributes, and common significance levels of 0.05 or 0.01.

1. Degrees
Sl. Level of
Test Formula of
No. Significance
Freedom
Chi Square Test
Test for As per given in
1 Goodness of the question or (n-1)
Fit: else 0.05.
E=
Test for
independence As per given in
2. the question or (r-1)(c-1)
of attributes E=
else 0.05.
T-Test
As per given in
t=
Test for Single the question or
Mean else 0.05.
3 (n-1)
S= (Depends on the
type of tail of
test)
As per given in
t=
Test for the question or
difference else 0.05.
4 (m+n-2)
mean (Depends on the
S= type of tail of
test)
t= As per given in
Test for Paired the question or
5 (n-1)
t Test else 0.05.
S=
(Depends on the
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2. type of tail of
test)
F – Test
f= if,
or (m-1,n-1)
Test for
6 0.05. or
Variance
f= if, (n-1,m-1)
Z – Test
Test for Single
Z= 0.05 = 1.96
7 mean Or Nil
0.01 = 2.58
Test for
Z= 0.05 = 1.96
8 difference of Or Nil
mean 0.01 = 2.58
Test for Z= 0.05 = 1.96
9 Or Nil
proportion
0.01 = 2.58
Z=
Test for
0.05 = 1.96
10 difference of Or Nil
proportion 0.01 = 2.58
P=
Run Test
Z=
0.05 = 1.96
11 Run Test Or Nil
E= 0.01 = 2.58
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3. =
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