A great explanation of hypothesis testing

1. © 1999 Prentice-Hall, Inc. Chap. 8 - 1
•General procedure for
hypothesis testing
Presentd by
Iram hassan

2. © 1999 Prentice-Hall, Inc. Chap. 8 - 2
A hypothesis is an
assumption about the
population parameter.
 A parameter is a
Population mean or
proportion
 The parameter must be
identified before
analysis.
I assume the mean GPA
of this class is 3.5!
© 1984-1994 T/Maker Co.
What is a Hypothesis?

3. © 1999 Prentice-Hall, Inc. Chap. 8 - 3
• States the Assumption (numerical) to be tested
e.g. The average # TV sets in US homes is at
least 3 (H0:  3)
• Begin with the assumption that the null
hypothesis is TRUE.
(Similar to the notion of innocent until proven guilty)
The Null Hypothesis, H0
•Always contains the ‘ = ‘ sign
•The Null Hypothesis may or may not be rejected.

4. © 1999 Prentice-Hall, Inc. Chap. 8 - 4
• Is the opposite of the null hypothesis
e.g. The average # TV sets in US homes is
less than 3 (H1:  < 3)
• Never contains the ‘=‘ sign
• The Alternative Hypothesis may or may
not be accepted
The Alternative Hypothesis, H1

5. © 1999 Prentice-Hall, Inc. Chap. 8 - 5
Steps:
 State the Null Hypothesis (H0:  3)
 State its opposite, the Alternative
Hypothesis (H1:  < 3)
 Hypotheses are mutually exclusive &
exhaustive
 Sometimes it is easier to form the
alternative hypothesis first.
Identify the Problem

6. © 1999 Prentice-Hall, Inc. Chap. 8 - 6
Population
Assume the
population
mean age is 50.
(Null Hypothesis)
REJECT
The Sample
Mean Is 20
Sample
Null Hypothesis
50?
20 

 
X
Is
Hypothesis Testing Process
No, not likely!

7. © 1999 Prentice-Hall, Inc. Chap. 8 - 7
• The significance level of a test is the
probabilty used as a standard rejecting a null
hypothesis Ho when Null Hypothesis Is True
 Called Rejection Region of Sampling
Distribution
• Designated a (alpha)
 Typical values are 0.01, 0.05, 0.10
• Selected by the Researcher at the Start
• Provides the Critical Value(s) of the Test
2.Level of Significance, a

8. © 1999 Prentice-Hall, Inc. Chap. 8 - 8
Level of Significance, aand
the Rejection Region
H0:  3
H1:  < 3
0
0
0
H0:   3
H1:  > 3
H0:  3
H1:   3
a
a
a/2
Critical
Value(s)
Rejection
Regions

9. © 1999 Prentice-Hall, Inc. Chap. 8 - 9
• Type I Error
 Reject True Null Hypothesis
 Has Serious Consequences
 Probability of Type I Error Is a
 Called Level of Significance
• Type II Error
 Do Not Reject False Null Hypothesis
 Probability of Type II Error Is b (Beta)
Errors in Making Decisions

10. © 1999 Prentice-Hall, Inc. Chap. 8 - 10
H0: Innocent
Jury Trial Hypothesis Test
Actual Situation Actual Situation
Verdict Innocent Guilty Decision H0 True H0 False
Innocent Correct Error
Do Not
Reject
H0
1 - a
Type II
Error (b )
Guilty Error Correct Reject
H0
Type I
Error
(a )
Power
(1 - b)
Result Possibilities

11. © 1999 Prentice-Hall, Inc. Chap. 8 - 11
• A test of statistics is a rule or procedure by
which sample results are used to decide
whethere to accept or reject the null
hypothesis.
• e.g: z test,t test,f test,ANOVA etc
3.Test Statistics

12. © 1999 Prentice-Hall, Inc. Chap. 8 - 12
• Probability of Obtaining a Test Statistic
More Extreme  or ) than Actual
Sample Value Given H0 Is True
• Called Observed Level of Significance
 Smallest Value of a H0 Can Be Rejected
• Used to Make Rejection Decision
 If p value a Do Not Reject H0
 If p value < a, Reject H0
p Value Test

13. © 1999 Prentice-Hall, Inc. Chap. 8 - 13
4.Critical region
• determine the rejection or crtical region n
such a way that the probabilty of rejecting
the null hypothesis Ho,if it is true,is equal to
the significance level,α.the location of the
crtical region depends upon the form of
H1.the significance level will seperate the
acceptance region from the rejection region.
• one tail and two tail test

14. © 1999 Prentice-Hall, Inc. Chap. 8 - 14
1. State H0 H0 : 3
2. State H1 H1 : <3
3. Choose a a = .05
4. Choose n n = 100
5. Choose Test: Z Test (or p Value)
Hypothesis Testing: Steps
Test the Assumption that the true mean #
of TV sets in US homes is at least 3.

15. © 1999 Prentice-Hall, Inc. Chap. 8 - 15
5.computation/calculation
compute the value of test statistics from
the sample data in order to decide
whethere to accept or reject the null
hypothesis.

16. © 1999 Prentice-Hall, Inc. Chap. 8 - 16
6.Decision
a.reject the null hypothesis Ho,if computed
value of the test statistics falls in the
rejection region and conclude that
Ho is true
b.accept the null hypothesis Ho,otherwise.

17. © 1999 Prentice-Hall, Inc. Chap. 8 - 17
Z
0
a
Reject H0
Z
0
Reject H0
a
H0: 
H1:  < 0
H0: 0
H1:  > 0
Must Be Significantly
Below = 0
Small values don’t contradict H0
Don’t Reject H0!
Rejection Region

18. © 1999 Prentice-Hall, Inc. Chap. 8 - 18
a= 0.025
n = 25
Critical Value: 1.645
Test Statistic:
Decision:
Conclusion:
Do Not Reject at a = .05
No Evidence True Mean
Is More than 368
Z
0 1.645
.05
Reject
Example Solution: One Tail
H0: 368
H1:  > 368
50
.
1



n
X
Z



19. © 1999 Prentice-Hall, Inc. Chap. 8 - 19
0 1.50 Z
Reject
(p Value = 0.0668)  (a = 0.05).
Do Not Reject.
p Value = 0.0668
a= 0.05
Test Statistic Is In the Do Not Reject Region
p Value Solution