1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
Welcome

2. A note on doodling

3. Before next exam (March 3rd)
Schedule of readings
Before next exam (March 3rd)
Please read chapters in OpenStax textbook
Please read Chapters 10, 11, 12 and 14 in Plous
Chapter 10: The Representativeness Heuristic
Chapter 11: The Availability Heuristic
Chapter 12: Probability and Risk
Chapter 14: The Perception of Randomness

4. By the end of lecture today 2/17/17
Counting ‘standard deviationses’ – z scores
Connecting raw scores, z scores and probability Connecting probability, proportion and area of curve
Percentiles

5. No New Homework Assignment
Just review assignments 10 & 11
Finding z scores and areas under the curve.
Both extended to Monday, February 20th

6. Lab sessions Everyone will want to be enrolled
in one of the lab sessions
Labs continue
With Project 2

7. Hand out z tables

8. z score = raw score - mean standard deviation
If we go up one standard deviation
z score = +1.0 and raw score = 105
z = -1
z = +1
68%
If we go down one standard deviation
z score = -1.0 and raw score = 95
If we go up two standard deviations
z score = +2.0 and raw score = 110
z = -2
95%
z = +2
If we go down two standard deviations
z score = -2.0 and raw score = 90
If we go up three standard deviations
z score = +3.0 and raw score = 115
99.7%
z = -3
z = +3
If we go down three standard deviations
z score = -3.0 and raw score = 85
z score: A score that indicates how many standard deviations
an observation is above or below the mean of the distribution
z score = raw score - mean
standard deviation

9. z table Formula Normal distribution Raw scores z-scores probabilities
Have z
Find raw score Z
Scores
Have z
Find area
z table
Formula
Have area
Find z
Area &
Probability
Have raw score
Find z
Raw Scores

10. Always draw a picture!
Homework worksheet

11. 1 .6800 1 sd 1 sd 28 30 32 Homework worksheet .6800 also fine: 68%
z =-1
z = 1 28 30 32

12. 2 .9500 2 sd 2 sd 26 28 30 32 34 Homework worksheet .9500
also fine: 95%
also fine:
.9500
2 sd
2 sd
z =-2
z = 2 26 28 30 32 34

13. 3 .9970 3 sd 3 sd 24 26 28 30 32 34 36 Homework worksheet .9970
also fine: 99.7%
also fine:
.9970
3 sd
3 sd
z =-3
z = 3 24 26 28 30 32 34 36

14. 4 .5000 24 26 28 30 32 34 36 Homework worksheet .5000 also fine: 50%
z = 0 24 26 28 30 32 34 36

15. 5 .4332 24 26 28 30 32 34 36 Homework worksheet z = 33-30 z = 1.5
Go to
table
.4332 2 5
also fine: %
.4332
z = 1.5 24 26 28 30 32 34 36

16. z =
33-30 2
z = 1.5
Go to
table
.4332
Add area
Lower half
= .9332 6
also fine: %
.9332
.4332
.5000
z = 1.5 24 26 28 30 32 34 36

17. 7 .4332 .0668 24 26 28 30 32 34 36 Homework worksheet z = 33-30 = 1.5
= 1.5
Go to
table
.4332
Subtract
from .5000
= .0668 2 7
also fine: 6.68%
.4332
.0668
z = 1.5 24 26 28 30 32 34 36

18. z =
29-30 2
= -.5
Go to
table
.1915
Add to upper
Half of curve
= .6915 8
also fine: %
.6915
.1915
.5000
z = -.5 24 26 28 30 32 34 36

19. =
25-30 2
= -2.5
.4938
Go to table =
31-30 2
=.5
.1915
Go to table
= .6853 9
also fine: %
.6853
.1915
.4938
z =-2.5
z = .5 24 26 28 30 32 34 36

20. z =
27-30 2
= -1.5
Go to
table
.4332
Subtract
From .5000
= .0668 10
also fine: 6.68%
.5000
.0668
.4332
z =-1.5 24 26 28 30 32 34 36

21. z =
25-30 2
= -2.5
Go to
table
.4938
Add lower
Half of curve
= .9938 11
also fine: %
.9938
.5000
.4938
z =-2.5 24 26 28 30 32 34 36

22. z =
32-30 2
= 1.0
Go to
table
.3413
Subtract
from .5000
= .1587 12
.5000
also fine: %
.1587
.3413
z =1 24 26 28 30 32 34 36

23. 13 24 26 28 30 32 34 36 50th percentile = median 30 In a normal curve
Median= Mean = Mode
z =0 24 26 28 30 32 34 36

24. 28 32 14
.6800
1 sd
1 sd
z =-1
z = 1 24 26 28 30 32 34 36

25. z table provides area from mean to score
x = mean + z σ = 30 + (.74)(2) = 31.48
77th percentile
Find area
of interest
= .2700
Find nearest z = .74 15
.2700
.7700
z table provides area from mean to score
.5000
31.48
z =.74 24 ? 30 36

26. z table provides area from mean to score
13th percentile
Find area
of interest
= .3700
Find nearest z = -1.13
x = mean + z σ = 30 + (-1.13)(2) = 27.74 16
Note:
=.50
z table provides area from mean to score
.3700
.1300
z =-1.13
27.74 ? 24 30 36

27. Please use the following distribution with
a mean of 200 and a standard deviation of 40. 80
120
160
200
240
280
320

28. 17 .6800 1 sd 1 sd 160 200 240 .6800 also fine: 68% also fine: .6826
z =-1
z = 1
160
200
240

29. 18 .9500 2 sd 2 sd 120 200 280 .9500 also fine: 95% also fine: .9544
z =-2
z = 2
120
200
280

30. 19 .9970 3 sd 3 sd 80 200 320 .9970 also fine: 99.7% also fine: .9974
z =-3
z = 3 80
200
320

31.
Go to
table =
= .75
.2734 40 20
also fine: %
.2734
z =.75 80
120
160
200
240
280
320

32. Go to
table
Add to upper
Half of curve
z = 40
= -.5
.1915
= .6915 22
also fine: %
.5000
.1915
.6915
z =-.5 80
120
160
200
240
280
320

33. z = 40
= 0.9
Go to
table
.3159
Subtract
from .5000
= .1841 23
.3159
also fine: %
.1841
z =.9 80
120
160
200
240
280
320

34. z = 40
= -.2
.0793
Go to table
= .2881
z = 40
=.55
.2088
Go to table 24
also fine: %
.2881
.2088
.0793
z =-.2
z =.55 80
120
160
200
240
280
320

35. = .9693
z =
= 1.875
Go to
table
Add area
Lower half
.4693 or
.4699
= .9699 40 25
Please note:
If z-score rounded to 1.88,
then percentile = 96.99%
also fine: %
.9693
.4693
.5000
z =1.875 80
120
160
200
240
280
320

36. Add area
Lower half
= .0089
= .0087
z = 40
z = 2.375
Go to
table
.4911 or
.4913 26
Please note:
If z-score rounded to 2.38,
then area = .0087
also fine: 0.89%
.4911
.0089
z =2.375 80
120
160
200
240
280
320

37. z = 40
= -1.75
.4599
Add to upper
Half of curve
Go to
table
= .9599 27
also fine: %
.9599
.5000
.4599
z =-1.75 80
120
160
200
240
280
320

38. 40
z =
= -1.75
.4599
Subtract
from .5000
= .0401
Go to
table 28
.0401
.4599
.5000
also fine: 4.01%
z =-1.75 80
120
160
200
240
280
320

39. z table provides area from mean to score
x = mean + z σ = (2.33)(40) = 293.2
99th percentile
Find area
of interest
= .4900
Find nearest z = 2.33 29
.4900
.9900
z table provides area from mean to score
.5000
293.2
z =2.33 80 ?
120
160
200
240

40. z table provides area from mean to score
33rd percentile
Find area
of interest
= .1700
Find nearest z = .44
x = mean + z σ = (-.44)(40) = 182.4 30
z table provides area from mean to score
Note:
=.50
.3300
.1700
182.4
z =-.44 ? 80
200
240
280
320

41. z table provides area from mean to score
40th percentile
Find area
of interest
= .1000
Find nearest z = -.25
x = mean + z σ = (-.25)(40) = 190 31
z table provides area from mean to score
Note:
=.50
190
.1000
.4000
z =-.25 ? 80
200
240
280
320

42. z table provides area from mean to score
67th percentile
Find area
of interest
= .1700
Find nearest z = .44
x = mean + z σ = (.44)(40) = 217.6 32
z table provides area from mean to score
.1700
z =.44 80
200
217.6 ?
320

43. Thank you!
See you next time!!