1. Quantitative Methods
HYPOTHESIS TESTING

2. How to determine if the test is a left
tailed, right tailed, or two-tailed test
• The type of test is determined by the
Alternative Hypothesis ( H1 )
• Left Tailed Test
• H1: parameter < value
Notice the inequality points to the left
• Decision Rule: Reject H0 if t.s. < c.v.

3. For Less Than Type or Left Tailed Test

4. For More Than Type or Right Tailed
Test
• The type of test is determined by the
Alternative Hypothesis ( H1 )
• Right Tailed Test
• H1: parameter > value
Notice the inequality points to the right
• Decision Rule: Reject H0 if t.s. > c.v.

5. For Greater Than Type or Right-Tailed
Test

6. For Not Equal To Type or TwoTailed
Test
• Two Tailed Test
• H1: parameter not equal value
Another way to write not equal is < or >
Notice the inequality points to both sides
• Decision Rule: Reject H0 if t.s. < c.v. (left) or t.s. > c.v. (right)
•
The decision rule can be summarized as follows:
• Reject H0 if the test statistic falls in the critical region
• (Reject H0 if the test statistic is more extreme than the
critical value)

7. Two Tailed Test

8. Tests For Means –Single
population
• Claim made by supplier that average contents
of a pack of rice is 50Kg
• Claim made by an Exporter that the collar size
of shirts in a consignment is 42 cms
• Claim made by an accountant that average
number of errors per a current a/c statement
is at the most one

9. • Let µ be average content of the pack
The Hypothesis to be tested is
H0 : µ = 50
Ha : µ <50
• Let µ be collar size in export consignment.
The Hypothesis to be tested is
H0 : µ =42
Ha : µ ≠ 42
• Let µ be average No. of errors per statement
The Hypothesis to be tested is
H0 : µ ≤1
Ha : µ >1

10. Tests For Proportions–Single population
• Claim made by the floor supervisor that
proportion of defective items produced by a
machine is at the most 1%
• Claim made by the branch manager of a bank
that proportion of customers experiencing
helping attitude of branch employees is 80%
• Claim made by a market researcher that
proportion of customers preferring colgate
toothpaste is 40%

11. • Let P be proportion of defective items produced
The Hypothesis to be tested is
H0 : P≤1%
Ha : P>1%
• Let P be proportion of customers experiencing helping
attitude
The Hypothesis to be tested is
H0 : P= 80%
Ha :P <80%
• Let P be proportion of customers preferring colgate
The Hypothesis to be tested is
H0 : P =40%

12. Tests For Means –Two populations
• Average sales after release of advertisement
have gone up
• Average sales in Mumbai are not the same as
those in Delhi
• Average number of patients suffering from
Malaria have gone down after regular
spraying of DDT by municipal corporation
• Results of new weight loss programme are
different from the old weight loss programme

13. • Let µ1be average sales before Advertisement
• Let µ2be average sales after Advertisement
• The test is
H0 : µ1 - µ2= 0 OR H0 : µ1 = µ2
Ha :µ1 - µ2 < 0 OR Ha :µ1 < µ2
• Let µ1be average sales in Mumbai
• Let µ2be average sales in Delhi
• The test is
H0 : µ1 - µ2= 0 OR H0 : µ1 = µ2
Ha :µ1 - µ2 ≠0 OR Ha :µ1 ≠µ2
• Let µ1be average No of patients with Malaria before DDT Spray
• Let µ2be average No of patients with Malaria afterDDT Spray
• The test is
H0 : µ1 - µ2= 0 OR H0 : µ1 = µ2
Ha :µ1 - µ2 >0 OR Ha :µ1 >µ2

14. Tests For Proportions–Two population
• Proportion of defectives has gone down after
introduction of new machine
• Proportion of customers satisfied with bank
service has gone up after training in
behavioral science imparted to its employees
• Proportion of consumers who prefer coke is
different from the proportion who prefer
pepsi

15. • Let P1be Proportion of defectives before introduction of new machine
• Let P2be Proportion of defectives after introduction of new machine
• The test is
H0 : P1 - P2= 0 OR H0 : P1 = P2
Ha :P1 - P2 >0 OR Ha :P1 >P2
• Let P1be Proportion of satisfied customers before training
• Let P2be Proportion of satisfied customers after training
• The test is
H0 : P1 - P2= 0 OR H0 : P1 = P2
Ha :P1 - P2 <0 OR Ha :P1 < P2
• Let P1be Proportion of consumers who prefer coke
• Let P2be Proportion of consumers who prefer pepsi
• The test is
H0 : P1 - P2= 0 OR H0 : P1 = P2
Ha :P1 - P2 ≠0 OR Ha :P1 ≠ P2