2. Practice
You wonder if psychology majors have higher IQs than sociology majors ( = .05)
You give an IQ test to 4 psychology majors and 4 sociology majors

3. Results
Psychology
110
150
140
135
Sociology 90 95 80 98

4. Step 1: Hypotheses Alternative hypothesis Null hypothesis
H1: psychology > sociology
Null hypothesis
H0: psychology = or < sociology

5. Step 2: Calculate the Critical t
df = N1 + N2 - 2
df = = 6
 = .05
One-tailed
t critical = 1.943

6. Step 3: Draw Critical Region
tcrit = 1.943

7. Now Step 4: Calculate t observed
tobs = (X1 - X2) / Sx1 - x2

8. Sx1 - x2 = X1= 535 X12= 72425 N1 = 4 X1 = 133.75 X2= 363
33129 4 4
4 (4 - 1)

9. X1= 535
X12= 72425
N1 = 4
X1 =
X2= 363
X22= 33129
N2 = 4
X2 = 90.75
9.38 =
363
535
72425
33129 4 4
4 (4 - 1)

10. Step 4: Calculate t observed
4.58 = ( ) / 9.38
Sx1 - x2 = 9.38
X1 =
X2 = 90.75

11. Step 5: See if tobs falls in the critical region
tcrit = 1.943
tobs = 4.58

12. Step 6: Decision If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

13. Step 7: Put answer into words
We Reject H0, and accept H1
Psychology majors have significantly ( = .05) higher IQs than sociology majors.

15. What if
The two samples have different sample sizes (n)

16. Results
Psychology
110
150
140
135
Sociology 90 95 80 98

17. Results
Psychology
110
150
140
135
Sociology 90 95 80

18. If samples have unequal n
All the steps are the same!
Only difference is in calculating the Standard Error of a Difference

19. Standard Error of a Difference
When the N of both samples is equal
If N1 = N2:
Sx1 - x2 =

20. Standard Error of a Difference
When the N of both samples is not equal
If N1 = N2:
N1 + N2 - 2

21. Results Psychology 110 150 140 135 Sociology 90 95 80 X1= 535
N1 = 4
X2= 265
X22= 23525
N2 = 3

22. X1= 535
X12= 72425
N1 = 4
X2= 265
X22= 23525
N2 = 3
N1 + N2 - 2

23. X1= 535
X12= 72425
N1 = 4
X2= 265
X22= 23525
N2 = 3
265
535
N1 + N2 - 2

24. X1= 535
X12= 72425
N1 = 4
X2= 265
X22= 23525
N2 = 3
265
535
23525
72425
N1 + N2 - 2

25. X1= 535
X12= 72425
N1 = 4
X2= 265
X22= 23525
N2 = 3
265
535
23525
72425 3 4 4 3

26. X1= 535
X12= 72425
N1 = 4
X2= 265
X22= 23525
N2 = 3
265
535
23525
72425 3 4 4 3 5

27. X1= 535
X12= 72425
N1 = 4
X2= 265
X22= 23525
N2 = 3
265
535
23525
72425
(.58) 3 4 4 3 5

28. = 10.69 X1= 535 X12= 72425 N1 = 4 X2= 265 X22= 23525 N2 = 3
72425
114.31 3 4 4 3 5
= 10.69

30. Practice
I think it is colder in Philadelphia than in Newport ( = .10).
To test this, I got temperatures from these two places on the Internet.

31. Results
Philadelphia 52 53 54 61 55
Newport 77 75 67

32. Hypotheses Alternative hypothesis Null hypothesis
H1: Philadelphia < Newport
Null hypothesis
H0:  Philadelphia = or >  Newport

33. Step 2: Calculate the Critical t
df = N1 + N2 - 2
df = = 6
 = .10
One-tailed
t critical =

34. Step 3: Draw Critical Region
tcrit = -1.44

35. Now Step 4: Calculate t observed
tobs = (X1 - X2) / Sx1 - x2

36. Standard Error of a Difference
When the N of both samples is not equal
If N1 = N2:
N1 + N2 - 2

37. X1= 275
X12= 15175
N1 = 5
X1 = 55
X2= 219
X22= 16043
N2 = 3
X2 = 73
219
275
16043
15175 3 5 5 3

38. = 3.05 X1= 275 X12= 15175 N1 = 5 X1 = 55 X2= 219 X22= 16043
15987
15175
15125 3 5 5 3 6
= 3.05

39. Step 4: Calculate t observed
-5.90 = ( ) / 3.05
Sx1 - x2 = 3.05
X1 = 55
X2 = 73

40. Step 5: See if tobs falls in the critical region
tcrit = -1.44
tobs = -5.90

41. Step 6: Decision If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

42. Step 7: Put answer into words
We Reject H0, and accept H1
Philadelphia is significantly ( = .10) colder than Newport.