1. Lecture 3 Section 1.4.1 – 1.4.2 Mon, Aug 30, 2004
What’s in the Bag?
Lecture 3
Section – 1.4.2
Mon, Aug 30, 2004

2. Outline Example of two bags Decision rule Acceptance region
Rejection region
Critical values
Relationship between  and 

3. Two Bags
Bag A
-1000 10 20 30 40 50 60
1000
Bag B
-1000 10 20 30 40 50 60
1000

4. The Hypotheses
H0: The shown bag is Bag A.
H1: The shown bag is Bag B.

5. Decisions and Errors H0 true H0 false Win $1890 Lose $560 Accept H0
Reject H0

6. Decision Rules
Decision Rule – A formal rule that tells us when to reject the null hypothesis.

7. Possible Decision Rules
Reject H0 if the voucher is worth $1000.
Decision Rule #1
Reject H0 if the voucher is worth either $60 or $1000, i.e.,  $60.

8. Rejection and Accepance Regions
Rejection Region – The set of values for which we would reject H0 .
Acceptance Region – The set of values for which we would accept H0 .
Critical Value – The value that separates the rejection region from the acceptance region.

9. Decision Rule #1
$60

10. Decision Rule #1
$60
Rejection
Region

11. Decision Rule #1
$60
Rejection
Region
Acceptance Region

12. Decision Rule #1
Rejection
Region
Acceptance Region
$60
Critical Value

13. Most Extreme Value
Direction of Extreme – The direction in which are found the values that are least likely under H0 but at the same time are very likely under H1.
Most Extreme Value – The value that is least likely under H0 but is very likely under H1.

14. Another Decision Rule Decision Rule #2
Reject H0 if the voucher is worth  $50.

15.  vs.  If we decrease , we will increase , and
Is it possible to decrease both  and  at the same time?

16. Let’s Do It!
Example 1.5, p. 21 – One-Sided Rejection Region to the Left.
Let’s do it! 1.6, p. 23 – Enlarging the Rejection Region.
Example 1.6, p. 24 – Two-Sided Rejection Region to the Left and to the Right.