1. Statistical Test of
Hypothesis

2. STATISTICS
DATA
central tendency
variability
distributions
graphical
representation
HYPOTHESIS
TESTING
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is the study of
has
can be
classified
into
are displayed with
is tested with

3. Statistical test of hypothesis
step by step process
used to verify a claim
using data
from a
scientific study

4. Statistically significant
a result that has been predicted as unlikely
to have occurred by chance alone,
according to a significance level.
Significance levell α (read as alpha)
a pre-determined threshold probability for a
test of hypothesis.
Definitions

5. hypothesis is a tentative explanation for an observation,
phenomenon, or scientific problem that
can be tested by further investigation.
In other words a scientific guess.
Two classifications
Null Hypothesis (HO) Alternative Hypothesis (HA)
status quo or default position
maintained hypothesis or
research hypothesis
-no relationship between two
measured phenomena
- that a treatment has no effect
-no difference when compared
- relationship exist
- treatment has effect
-significant difference when compared
already accepted accepted only when the null hypothesis is rejected
denoted by
= equality
denoted by
≠ only concerned that null hypothesis is not true.
>, < direction is important

6. Process
Problem or Claim is posted
Null Hypothesis Alternative Hypothesis
are formulated
step 1
significance levelstep 2 is agreed upon
critical value* is determined
step 3 Appropriate Test* is identified and applied
step 4 Conclusions
are made by comparing test result and critical
value
"Null hypothesis is either accepted or rejected"
step 5 INTERPRETATION problem is solved or claim is verified

7. Interpretation of Significance level
Significance level Interpretation
α≤ .01 very strong evidence against the null hypothesis
.01< α ≤ .05 moderate evidence against the null hypothesis
.05< α ≤ .10 suggestive evidence against tthe null hypothesis
α> .10 little or no real evidence against tthe null hypothesis

9. Large-Sample Tests of Hypothesis
Population Mean vs Sample Mean
Population
samplesample
xHo =µ:
xHa
xHa
xHa
<
>
≠
µ
µ
µ
:
:
:
Assumptions:
Large sample (n ≥ 30)
Sample is randomly selected

10. Testing Population Mean
Example:
Test the hypothesis that weight loss in a new diet program exceeds 20 pounds during the
first month.
Sample data : n = 36, mean = 21, s = 5, μ0 = 20, α = 0.05
Assumptions:
Large sample (n ≥ 30)
Sample is randomly selected n
s
x
z 0µ−
=
test statistics
Solution:
Step1 : H0 : μ = 20 (μ is not larger than 20)
Ha : μ > 20 (μ is larger than 20)
Step2 : α = 0.05 zα (critical value) =1.645

11. 20.1
)6(
5
1
36
5
2021
0
+=
=
−
=
−
=
z
z
z
n
s
x
z
µ
Testing Population Mean
Step3 : Z test since n ≥ 30
Step4: Decision: Accept Ho
Conclusion: At 5% significance level there is insufficient statistical evidence to conclude
that weight loss in a new diet program exceeds 20 pounds per first month.

12. population 2 or
sample 2
population 2 or
sample 2
population 1 or
sample 1
Test Concerning Two Means
Population vs Population or Sample vs Sample
population 1 or
sample 1
21
21
:
:
xxHo
Ho
=
= µµ
2121
2121
2121
:,:
:,:
:,:
xxHaHa
xxHaHa
xxHaHa
<<
>>
≠≠
µµ
µµ
µµ

13. Comparing Two Population Means
Example: A random sample of 35 baby boys showed a mean birth weight of 7.4 lbs with a
standard deviation 1.18 lbs while 40 baby girls showed a mean birth weight of 6.5 lbs
with a standard deviation 1.5 lbs. Test if there are gender differences at 1% level of
significance.
Assumptions:
1. Large samples ( n1 ≥ 30; n2 ≥ 30)
2. Samples are randomly selected
3. Samples are independent 2
2
2
1
2
1
21
nn
xx
z
σσ
+
−
=
test statistics
Solution:
Step1 : H0 : μ1 = μ2 (no gender difference)
Ha : μ1 ≠ μ2 (there is gender difference)
Step2 : α = 0.01 zα (critical value) =+/-2.58

14. Comparing Two Population Means
Step3 : z test ( n1 ≥ 30; n2 ≥ 30)
2.9042
0.0960
9.0
40
(1.5)
35
(1.18)
6.57.4
22
2
2
2
1
2
1
21
==
+
−
=
+
−
=
nn
xx
z
σσ
Step4: Decision: Reject Ho
Conclusion:There is sufficient evidence to conclude that there is a significant
difference in the birthweight between boys and girls at 1% level of significance

15. Large-Sample Tests of Hypothesis
• Other tests
–Testing a Population Proportion
–Comparing Two Population Proportions
are left as part of research

16. End of
First Part of the
Discussions

17. Review
Exercises

18. Review Exercises
1. Ambulatory Services Inc. claims that their average response time is within 30 minutes
of receipt of call. The response time for a random sample of 64 cases were recorded,
with a sample mean of 34 minutes and a standard deviation of 21 minutes.
(i) Is there sufficient evidence to conclude that the actual response time is
larger than what is claimed by Ambulatory Services Inc.? Use α = .05
2. A chemist from a university claimed that he has invented a new spray that will keep the
flowers fresh longer. He based his claim on a test when he selected 500 blossoms of
a single type of flower and placed into two groups. One group (consisting of 250
blossoms) was sprayed with his formulation and the other with no spray. For the
treatment he found that the average wilting time was 7.2 days with a standard
deviation of 1.2 days, while for the control group, 3.6 days with a standard deviation
of 1.1 days. Do you agree with the claim of the chemist that the spray actually keeps
the flowers fresh longer? Use α = .01
3. A pharmaceutical company claims that they have developed a new drug that will
provide immediate relief for persons suffering from vertigo. VERTIPLUS is claimed to
provide relief within 5 minutes. A clinical trial was undertaken to test this claim and out
of 36 tests the mean relief time is recorded at 6.7 minutes with a standard deviation of
1.38 minutes. Is there sufficient evidence to uphold the claim? α = .01
.

19. THANK YOU!