2. TESTING THE SIGNIFICANT DIFFERENCE
BETWEEN
Population or hypothesized mean, that is
Population mean vs Sample mean
Two sample means and two sample standard
deviations are known, that is Sample mean1 vs
Sample mean 2
Two sample means and population standard
deviation is known, that is Sample mean 1 vs
Sample mean 2
3. TESTING THE SIGNIFICANCE BETWEEN
MEANS
“ n is large or when n ≥ 30 and σ is known”
Population mean vs Sample mean
4. TESTING THE SIGNIFICANCE OF DIFFERENCE
BETWEEN MEANS
“n is large or when n ≥ 30 and σ is unknown”
Sample mean 1 vs Sample mean 2 and 2 sample
standard deviations are known.
5. TESTING THE SIGNIFICANCE OF DIFFERENCE
BETWEEN MEANS
“n is large or when n ≥ 30 and σ is known”
Sample mean 1 vs Sample mean 2 and population
standard deviation is known.
6. EXAMPLE 1
The average score in the final examination in College
Algebra at ABC College is known to be 80 with a
standard deviation of 10. A random sample of 39
students was taken from this year’s batch and it
was found that they have a mean score of 84. Test
at 5% level of significance.
a. Is this an indication that this year’s batch
performed better in College Algebra than the
previous batches?
b. Is the mean score in College Algebra of this year’s
batch different from 80?
7. EXAMPLE 2
The dean of ABC College wants to know which
method is better in teaching Chemistry. He took a
random sample of 40 students handled by only one
teacher in lecture and laboratory, and found it to
have a mean final grade of 83 with a standard
deviation of 7. Fifty students from a group handled
by two different teachers in lecture and laboratory
were randomly taken and it was found that they
have a mean final grade of 87 with a standard
deviation of 10. Does this indicate that a two-
teacher setup is better than a one-teacher setup?
Test at α =0.01
8. EXAMPLE 3
A Statistics teacher wants to know if students exposed to the
use of technology in the classroom got significantly higher
scores in Statistics exam than those who are exposed to the
traditional chalk and talk method.
She took a sample of 30 students exposed to technology and recorded
their Statistics exam scores:
95 88 81 98 81 80 83 80 91 80
75 83 88 85 81 85 83 86 89 88
90 89 88 85 87 86 66 85 65 95
She then took a sample of 40 students who were taught using the
traditional method
88 78 81 87 91 90 83 84 66 81
80 74 73 71 66 60 78 78 65 60
71 85 89 79 80 83 75 73 80 71
65 71 89 81 75 60 82 80 90 83
Help the teacher verify the hypothesis at α = 0.05.
9. EXERCISE
1. A random sample of 46 adult coyotes in a region of
northern Minnesota showed the average age to be
2.05 years, with sample standard deviation 0.82
years. However, it is thought that the overall
population mean age of coyotes is 1.75. Do the
sample data indicated that coyotes in this region of
northern Minnesota tend to live longer than the
average of 1.75 years? Use 0.01 level of significance.
