The document discusses the concept of standard error and its applications in hypothesis testing at different significance levels (5% and 1%). It classifies tests of significance into three types based on sample size—attributes, large samples, and small samples—and provides examples of their application in biological sciences. Additionally, it outlines the use of t-tests and f-tests for small samples to evaluate specific health and agricultural statistics.

1. K.SUDHA RAMESHWARI
ASSISTANT PROFESSOR,
V.V.VANNIAPERUMAL COLLEGE FOR WOMEN,VIRUDHUNAGAR
TAMILNADU,INDIA

2. The standard deviation of the
sampling distribution is called
standard error
The following is the list of formula for
obtaining standard error for different
statistics

6. Utility of standard error
 It is used as an instrument in testing a given hypothesis.
When the hypothesis is tested at 5% level of significance
, if the difference between observed and expected mean
is more than 1.96 standard error, we may conclude that
the result of the experiment does not support the
hypothesis at 5% level and if the difference is less than
1.96 SE, we can accept the hypothesis.
 At 1% significance level, if the difference is more than
2.58 SE, we can’t accept the hypothesisa and vice versa

7. Tests of significance can be
classified into three
1. Tests of significance for attributes
2. Tests if significance for variables (large
samples)
3. Tests of significance for variables
(small samples)

8. Application of tests of significance in
biological sciences
Tests of significance of attributes:
1. To find out whether both vegetarian and non-
vegetarian food eaters are equally intelligent
or not
2. To test the hypothesis that male and female
babies are born in equal number
When we take two samples from two different
populations, we can find out whether there is
any significant difference in the proportion of
success. Examples -To find out whether there
is any significant difference in the food habits
of two villagers

9. Tests of significance of large samples:
A sample is considered to be large when its size exceeds
30 (n>30)
The various fields of applications are:
1. To test the hypothesis that there is no significant
difference between sample mean height and
hypothetical mean height of sugarcane
2. To test the hypothesis that there is no significant
difference in the yield of grains between the two
varieties

10. 3.To test the hypothesis that there is no significant
difference between mean accidents in the two
towns
4. To test the hypothesis that there is no significant
difference in standard deviation of yield between
paddy and wheat
5. To test the hypothesis that Indian paddy plants are
on an average not taller than Australian paddy
plants

11. Tests of significance of small samples
 Small samples means (n<30) t-test and F-test are
applied
Applications of t-test are
1. To find out whether systolic blood pressure of a
sample of 10 persons in the age group of 40-50 is
significantly differ from the hypothetical value of
blood pressure of the population
2. To test the hypothesis that the average weight of goat
population is 12kgs.

12. Reference
 Statistical methods for biologists(Biostatistics)-
S.Palanichamy, M.Manoharan