1. INTEGRATED LEARNING CENTER
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Lecturer’s desk
Cabinet
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Computer Storage Cabinet 4 3
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INTEGRATED LEARNING CENTER
ILC 120
broken
desk

2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall, 2014 Room 120 Integrated Learning Center (ILC) 10: :50 Mondays, Wednesdays & Fridays.
Welcome

3. A note on doodling
Reminder

4. Labs continue this week
Lab sessions
Labs continue this week

5. One positive
correlation
One negative
correlation
One t-test

7. Schedule of readings Before next exam (October 17th)
Please read chapters 5, 6, & 8 in Ha & Ha
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

8. By the end of lecture today 10/8/14
Use this as your
study guide
By the end of lecture today 10/8/14
Counting ‘standard deviationses’ – z scores
Connecting raw scores, z scores and probability Connecting probability, proportion and area of curve
Percentiles

9. No homework due Friday (October 10th)

10. Raw scores, z scores & probabilities
Notice:
3 types of numbers
raw scores
z scores
probabilities
Mean = 50
Standard deviation = 10
z = -2
z = +2
If we go up two standard deviations
z score = +2.0 and raw score = 70
If we go down two standard deviations
z score = -2.0 and raw score = 30

11. 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

12. Raw scores, z scores & probabilities
Have z
Find area
Have z
Find raw score Z
Scores
z table
Formula
Have area
Find z
Area &
Probability
Have raw score
Find z
Raw Scores

13. .
Homework Worksheet

14. Hint: Always draw a picture!
Homework worksheet

15. .
Homework Worksheet: Problem 1
1 sd
1 sd
.68 28 30 32

16. .
Homework Worksheet: Problem 2
2 sd
2 sd
.95 26 28 30 32 34

17. .
Homework Worksheet: Problem 3
3 sd
3 sd
.997 24 26 28 30 32 34 36

18. .
Homework Worksheet: Problem 4
.50 24 26 28 30 32 34 36

19. .4332 Homework Worksheet: Problem 5 . 24 26 28 30 32 34 36 33-30 Go to
table
z =
z = 1.5
.4332 2
.4332 24 26 28 30 32 34 36

20. .9332 .4332 .5000 Homework Worksheet: Problem 6 . 24 26 28 30 32 34 36
33-30
Go to
table
z =
z = 1.5
.4332 2
.9332
.4332
.5000 24 26 28 30 32 34 36

21. .0668
33-30
Go to
table
.4332
z =
z = 1.5
.4332 2 33
= .0668
29-30
Go to
table
z =
z =-.5
.1915
.1915
.5000 2
= .6915 29
.4938
.1915
25-30 25 31
z =
z = -2.5
.4938 2
= .6853
31-30
Go to
table
z =
z =.5
.1915 2
.0668
.4332
27-30
z =
z = -1.5
.4332 27 2
= .0668

22. Homework Worksheet Problem 11: .5000 + .4938 = .9938
Problem 14: 28 and 32

23. .
77th percentile
Go to
table
nearest z = .74
.2700
x = mean + z σ = 30 + (.74)(2) = 31.48
.7700
.27
.5000 24 26 28 30 ? 34 36
31.48

24. .
13th percentile
Go to
table
nearest z = 1.13
.3700
x = mean + z σ = 30 + (-1.13)(2) = 27.74
Note:
= .50
.37
.50
.13 24 ? 26
27.74 30 32 34 36

25. Homework Worksheet Problem 17: 68% or .68 or 68.26% or .6826

26. .2734 Please use the following distribution with a mean of 200
and a standard deviation of 40.
Find the area under the curve between scores of 200 and 230.
Start by filling in the desired information on curve 20 (to the right) (Note this one will require you to calculate a z-score for a raw score of 230 and use the z-table)
Go to
table
z =
z = .75
.2734 40
.2734 80
120
160
200
240
280
320

27. Homework Worksheet Problem 21: 40.13% or .4013
Problem 25: % or or 96.93% or .9693
Problem 26: .89% or .0089
Problem 27: % or .9599
Problem 28: 4.01% or .0401
Problem 29:
x = mean + z σ = (2.33)(40) = 293.2
Problem 30:
x = mean + z σ = (-.44)(40) = 182.4
Problem 31: 190
Problem 32:

28. ? .9500 .4500 .5000 x = mean + z σ = 50 + (1.64)(4) = 56.56 Problem 7
Normal Distribution has a mean of 50 and standard deviation of 4.
Determine value below which 95% of observations will occur Note: sounds like a percentile rank problem
Go to
table
.4500
nearest z = 1.64
x = mean + z σ = 50 + (1.64)(4) = 56.56
.9500
.4500
.5000
Problem 7 38 42 46 50 54
56.60 ? 58 62

29. ? .4700 .0300 x = mean + z σ = 2100 + (-1.88)(250) = 1,630 Problem 8
Normal Distribution has a mean of $2,100 and s.d. of $250.
What is the operating cost for the lowest 3% of airplanes Note: sounds like a percentile rank problem = find score for 3rd percentile
Go to
table
.4700
nearest z =
x = mean + z σ = (-1.88)(250) = 1,630
.0300
.4700
Problem 8
1,630 ?
2100

30. Normal Distribution has a mean of 195 and standard deviation of 8.5.
Determine value for top 1% of hours listened.
Go to
table
.4900
nearest z = 2.33
x = mean + z σ = (2.33)(8.5) =
.4900
.5000
.0100
Problem 9
195
214.8 ?

31. ? .7500 .25 .5000 Find score associated with the 75th percentile .
Go to
table
nearest z = .67
.2500
x = mean + z σ = 30 + (.67)(2) = 31.34
.7500
.25
.5000 24 26 28 30 ? 34 36
31.34
z = .67
Problem 10

32. ? .2500 .25 .25 Find the score associated with the 25th percentile .
Go to
table
nearest z = -.67
.2500
x = mean + z σ = 30 + (-.67)(2) = 28.66
.2500
.25
.25 24 26
28.66 28 ? 30 34 36
z = -.67
Problem 11

33. Mean of 30 and standard deviation of 2.
Try this one:
Please find the (2) raw scores that border exactly the middle 95% of the curve
Mean of 30 and standard deviation of 2
Go to
table
.4750
nearest z = 1.96
mean + z σ = 30 + (1.96)(2) = 33.92
Go to
table
.4750
nearest z = -1.96
mean + z σ = 30 + (-1.96)(2) = 26.08
.9500
.475
.475
Problem 12
26.08
33.92 24 ? 28 30 32 ? 36

34. Thank you!
See you next time!!