Hypothesis testing is a statistical technique used to make decisions about a population based on sample data. In the case of continuous normal data, one may be interested in testing hypotheses about the mean and variance of the population from which the data were sampled. Testing Hypotheses about the Mean To test hypotheses about the mean of a population with continuous normal data, one may use a t-test. The t-test is a parametric test that compares the mean of the sample to a hypothesized value, typically denoted as μ0. The null hypothesis, denoted as H0, is that the population mean is equal to the hypothesized value, while the alternative hypothesis, denoted as Ha, is that the population mean is not equal to the hypothesized value.

1. Hypothesis Testing
Akshita Manwati
Tabassum Irfan
Harender Singh
Indrajeet Hulyalkar
Mayank Kumar
Vishal Gautam
Ashwani Kumar
PRN008
PRN073
PRN099
PRN100
PRN114
PRN015
PRN088
TEAM 7
Continuous Normal Data (Y) and
Variance tests with examples
6σ Presentation

2. Hyopthesis Testing
Alternate Hypothesis Ha Ha : Shortage of material impacts cycle time
Null Hpothesis H0 H0 : Shortage of material does not impact cycle time
Making an assumption, called hypothesis, about a population parameter
Example: Suppose we claim that cycle time for the machine is impacted by the shortage of material.
Alternate Hypothesis Ha
States the claims of effect because
of the cause are true.
Null Hpothesis H0
States the claims of effect because
of the cause are false.
Generally, we accept Ha as we want to prove our claims.
Ashwani

3. Choice of test - Continuous Normal Data and Variance tests
Here X is the cause and Y is the effect.
Y – Data Type
Continuous – Variation
Comparison
X - Data Type &
Level
No X, comparing with
historical variation value
Discrete – Binary –
2 levels
Discrete Ord. /Nominal –
more than 2 levels
Test
1 Variance Test
2 Variance
Test of Equal variance
Tabassum

4. Hypothesis Testing Steps
Define the
Alternative
Hypotheses
1
Deduce Null
from
alternate.
2
Determine
the level of
significance
3
Randomly
select a
representative
sample of data
4
Compute
and
Compare the
P-value
6
Select the
test
5
The steps involved in conducting hypothesis testing are as below:
Indrajeet

5. Y – Continuous & X - comparing with historical variation value
1 Variance Test
1. Define Alternate Hypothesis
Ha: Average delivery time =! 6
Problem Statement:
There are two vendor(P & Q) for delivering the item to the manufacturing
company. You are required to test the delivery time of the supplier, it is
traditionally assumed that supplier P provides the best delivery, but we need to
test that assumption against the supplier Q. Test the hypothesis on the mean
delivery time of 6 days and variance is 4.
2. Deduce null from alternate
Ho: Average delivery time = 6
3. Determine the level of significance
Confidence Level 95%
4. Randomly select a representative sample of data
A sample of 40 for the delivery time from vendor Q whereas for Vendor P we
have historical data
Vishal

6. Y – Continuous & X - comparing with historical variation value
1 Variance Test
Problem Statement:
………..It is traditionally assumed that supplier P provides the best delivery, but
we need to test that assumption against the supplier Q. Test the hypothesis
on the mean delivery time of 6 days and variance is 4.
5. Select the test
As the effect, Y – Continuous & cause, X – comparing with historical variation
value so we have selected 1-variance test
6. Compute and Compare the P-value
Here p-value = 0.932 as per Chi-square Method,
Since p >0.05
so, P-high null Fly !!!
We fail to reject Null Hypothesis Mayank

7. Y – Continuous & X – binary – 2 levels
2 Variance Test
1. Define Alternate Hypothesis
Ha: Variance of Machine 1 =! Variance of Machine 2
Problem Statement:
There are two moulding machine M1 and M2 producing same item. The cycle
time i.e., the amount of time spent on producing item on both machine are
listed. Test hypothesis are equal with 95% confidence.
2. Deduce null from alternate
Ho: Variance of Machine 1 = Variance of Machine 2
3. Determine the level of significance
Confidence Level 95%
Akshita

8. Y – Continuous & X – binary – 2 levels …..continued
2 Variance Test
4. Randomly select a representative sample of data
A sample of 20 from each machine M1 and M2 is taken.
Problem Statement:
There are two moulding machine M1 and M2 producing same item. The cycle
time i.e., the amount of time spent on producing item on both machine are
listed. Test hypothesis ae equal with 95% confidence
5. Select the test
As the effect, Y – Continuous & cause, X – binary – 2 levels(M1 and M2) so
we have selected 2-variance test
6. Compute and Compare the P-value
Here p-value = 1 as per Levene Method,
Since p >0.05
so, P-high null Fly !!!
We fail to reject Null Hypothesis Harender

9. Minitab Exercise
Objectives
Find out whether process is under Statistical Control or
not. If not, how many issues are there.
Day
No of
Invoices
Residence Address
incorrect
1 15 2
2 20 3
3 11 2
4 12 4
5 14 3
6 20 2
7 16 2
8 21 3
9 19 2
10 22 3
11 18 1
12 12 2
13 14 3
14 12 4
15 16 4
Determine the test
Sub-group size is variable
Defects are discrete
Hence, we will use U-Chart Control Test

10. Minitab Exercise
Inferences
Stat > Control Charts > Attributes Chart > U…
U=0.1653
That means 16.53%
chances are that the
invoices have wrong
residence address
• No subgroup is out of
Control limit.
• Point depicts random
pattern but no evidence for
lack of control.
Process is in Control

11. Connect with us in case of any doubt.
Email: harender.singh@siom.in
+919812969049
Thanks
Akshita Manwati
Tabassum Irfan
Harender Singh
Indrajeet Hulyalkar
Mayank Kumar
Vishal Gautam
Ashwani Kumar
PRN008
PRN073
PRN099
PRN100
PRN114
PRN015
PRN088