Download - Practice
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Practice
• You are interested in how citizens of the US feel about the president. You asked 8 people to rate the president on a 10 point scale. Describe how the country feels about the president -- be sure to report a measure of central tendency and the standard deviation.
8, 4, 9, 10, 6, 5, 7, 9
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Central Tendency
8, 4, 9, 10, 6, 5, 7, 9
4, 5, 6, 7, 8, 9, 9, 10
Mean = 7.25
Median = (4.5) = 7.5
Mode = 9
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Standard Deviation X X2
8 64
4 16
9 81
10 100
6 36
5 25
7 49
9 81
= 58 = 452
-1
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Standard Deviation X X2
8 64
4 16
9 81
10 100
6 36
5 25
7 49
9 81
= 58 = 452
-1
45258 8
8 - 1
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Standard Deviation X X2
8 64
4 16
9 81
10 100
6 36
5 25
7 49
9 81
= 58 = 452
-1
58452 8
8 - 1
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Standard Deviation X X2
8 64
4 16
9 81
10 100
6 36
5 25
7 49
9 81
= 58 = 452
-1
452 420.5
7
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Standard Deviation X X2
8 64
4 16
9 81
10 100
6 36
5 25
7 49
9 81
= 58 = 452
-1
2.12
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Variance
• The last step in calculating a standard deviation is to find the square root
• The number you are fining the square root of is the variance!
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Variance
S 2 =
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Variance
- 1S 2 =
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Practice• Below are the test score of Joe and Bob. What
are their means, medians, and modes? Who tended to have the most uniform scores (calculate the standard deviation and variance)?
• Joe
80, 40, 65, 90, 99, 90, 22, 50
• Bob
50, 50, 40, 26, 85, 78, 12, 50
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Practice
• Joe
22, 40, 50, 65, 80, 90, 90, 99
Mean = 67
• Bob
12, 26, 40, 50, 50, 50, 78, 85
Mean = 48.88
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Practice
• Joe
22, 40, 50, 65, 80, 90, 90, 99
Median = 72.5
• Bob
12, 26, 40, 50, 50, 50, 78, 85
Median = 50
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Practice
• Joe
22, 40, 50, 65, 80, 90, 90, 99
Mode = 90
• Bob
12, 26, 40, 50, 50, 50, 78, 85
Mode = 50
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Practice
• Joe
22, 40, 50, 65, 80, 90, 90, 99
S = 27.51; S2 = 756.80
• Bob
12, 26, 40, 50, 50, 50, 78, 85
S = 24.26; S2 = 588.55
Thus, Bob’s scores were the most uniform
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Review
• Ways to “see” data– Simple frequency distribution– Group frequency distribution– Histogram– Stem-and-Leaf Display– Describing distributions– Box-Plot
• Measures of central tendency– Mean – Median– Mode
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Review
• Measures of variability– Range– IQR– Standard deviation – Variance
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What if. . . .
• You recently finished taking a test that you received a score of 90 and the test scores were normally distributed.
• It was out of 200 points
• The highest score was 110
• The average score was 95
• The lowest score was 90
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Z-score
• A mathematical way to modify an individual raw score so that the result conveys the score’s relationship to the mean and standard deviation of the other scores
• Transforms a distribution of scores so they have a mean of 0 and a SD of 1
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Z-score
• Ingredients:
X Raw score
Mean of scores
S The standard deviation of scores
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Z-score
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What it does
• x - Tells you how far from the mean you are and if you are > or < the mean
• S Tells you the “size” of this difference
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Example
• Sample 1:
X = 8
= 6
S = 5
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Example
• Sample 1:
X = 8
= 6
S = 5
Z score = .4
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Example
• Sample 1:
X = 8
= 6
S = 1.25
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Example
• Sample 1:
X = 8
= 6
S = 1.25
Z-score = 1.6
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Example
• Sample 1:
X = 8
= 6
S = 1.25
Z-score = 1.6
Note: A Z-score tells you how many SD above or below a mean a specific score falls!
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Practice
• The history teacher Mr. Hand announced that the lowest test score for each student would be dropped. Jeff scored a 85 on his first test. The mean was 74 and the SD was 4. On the second exam, he made 150. The class mean was 140 and the SD was 15. On the third exam, the mean was 35 and the SD was 5. Jeff got 40. Which test should be dropped?
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Practice
• Test #1
Z = (85 - 74) / 4 = 2.75
• Test #2
Z = (150 - 140) / 15 = .67
• Test #3
Z = (40 - 35) / 5 = 1.00
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Practice
Time(sec)
Distance(feet)
Rachel 30 6
Joey 40 8
Ross 25 4
Monica 45 10
Chandler 33 9
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Did Ross do worse in the endurance challenge than in the throwing challenge? Did Monica do better in the throwing challenge than the endurance?
Time(sec)
Distance(feet)
Rachel 30 6
Joey 40 8
Ross 25 4
Monica 45 10
Chandler 33 9
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Practice
Time (sec)
Distance (feet)
Rachel 30 6
Joey 40 8
Ross 25 4
Monica 45 10
Chandler 33 9
= 34.6 = 7.4
S = 7.96 S = 2.41
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Practice
Time (sec)
Distance (feet)
Rachel 30 -.58 6
Joey 40 .68 8
Ross 25 -1.21 4
Monica 45 1.31 10
Chandler 33 -.20 9
= 34.6 = 7.4
S = 7.96 S = 2.41
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Practice
Time (sec)
Distance (feet)
Rachel 30 -.58 6 -.58
Joey 40 .68 8 .25
Ross 25 -1.21 4 -1.66
Monica 45 1.31 10 1.08
Chandler 33 -.20 9 .66
= 34.6 = 7.4
S = 7.96 S = 2.41
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Ross did worse in the throwing challenge than the endurance and Monica did better in the endurance than the throwing challenge.
Time (sec)
Distance (feet)
Rachel 30 -.58 6 -.58
Joey 40 .68 8 .25
Ross 25 -1.21 4 -1.66
Monica 45 1.31 10 1.08
Chandler 33 -.20 9 .66
= 34.6 = 7.4
S = 7.96 S = 2.41
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Shifting Gears
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Question
• A random sample of 100 students found:– 56 were psychology majors– 32 were undecided– 8 were math majors– 4 were biology majors
• What proportion were psychology majors?
• .56
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Question
• A random sample of 100 students found:– 56 were psychology majors– 32 were undecided– 8 were math majors– 4 were biology majors
• What is the probability of randomly selecting a psychology major?
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Question
• A random sample of 100 students found:– 56 were psychology majors– 32 were undecided– 8 were math majors– 4 were biology majors
• What is the probability of randomly selecting a psychology major?
• .56
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Probabilities
• The likelihood that something will occur
• Easy to do with nominal data!
• What if the variable was quantitative?
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Extraversion
BFISUR
4.88
4.63
4.38
4.13
3.88
3.63
3.38
3.13
2.88
2.63
2.38
2.13
1.88
1.63
1.38
1.13
Co
un
t50
40
30
20
10
0
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BFIOPN
5.00
4.80
4.60
4.40
4.20
4.00
3.80
3.60
3.40
3.20
3.00
2.80
2.60
2.40
2.20
2.00
1.60
Co
un
t
40
30
20
10
0
Openness to Experience
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BFISTB
4.88
4.50
4.25
4.00
3.75
3.50
3.25
3.00
2.75
2.50
2.25
2.00
1.75
1.50
1.25
Co
un
t40
30
20
10
0
Neuroticism
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Probabilities
Normality frequently occurs in many situations of psychology, and other sciences
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COMPUTER PROG
• http://www.jcu.edu/math/isep/Quincunx/Quincunx.html
• http://webphysics.davidson.edu/Applets/Galton/BallDrop.html
• http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
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Next step
• Z scores allow us to modify a raw score so that it conveys the score’s relationship to the mean and standard deviation of the other scores.
• Normality of scores frequently occurs in many situations of psychology, and other sciences
• Is it possible to apply Z score to the normal distribution to compute a probability?
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Theoretical Normal Curve
-3 -2 -1 1 2 3
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Theoretical Normal Curve
-3 -2 -1 1 2 3
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Theoretical Normal Curve
-3 -2 -1 1 2 3
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Theoretical Normal Curve
-3 -2 -1 1 2 3
Note: A Z-score tells you how many SD above or below a mean a specific score falls!
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Theoretical Normal Curve
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
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We can use the theoretical normal distribution to determine the probability of an event. For example, do you know the probability of getting a Z score of 0 or less?
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.50
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We can use the theoretical normal distribution to determine the probability of an event. For example, you know the probability of getting a Z score of 0 or less.
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.50
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With the theoretical normal distribution we know the probabilities associated with every z score! The probability of getting a score between a 0 and a 1 is
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.3413 .3413
.1587 .1587
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What is the probability of getting a score of 1 or higher?
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.3413 .3413
.1587 .1587
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These values are given in Appendix Z
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.3413 .3413
.1587 .1587
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-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.3413 .3413
.1587 .1587
Mean to Z
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-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.3413 .3413
.1587 .1587
Smaller Portion
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-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.84
.1587
Larger Portion
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Practice
• What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
• Between mean and z = .56?
• Above z = 2.25?
• Above z = -1.45
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Practice
• What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
• Between mean and z = .56?.2123
• Above z = 2.25?
• Above z = -1.45
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Practice
• What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
• Between mean and z = .56?.2123
• Above z = 2.25?.0122
• Above z = -1.45
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Practice
• What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
• Between mean and z = .56?.2123
• Above z = 2.25?.0122
• Above z = -1.45.9265
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Practice
• What proportion of this class would have received an A on the last test if I gave A’s to anyone with a z score of 1.25 or higher?
• .1056
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Example: IQ
• Mean IQ = 100
• Standard deviation = 15
• What proportion of people have an IQ of 120 or higher?
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Step 1: Sketch out question
-3 -2 -1 1 2 3
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Step 1: Sketch out question
-3 -2 -1 1 2 3
120
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Step 2: Calculate Z score
-3 -2 -1 1 2 3
120
(120 - 100) / 15 = 1.33
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Step 3: Look up Z score in Table
-3 -2 -1 1 2 3
120
Z = 1.33
.0918
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Example: IQ
• A proportion of .0918 or 9.18 percent of the population have an IQ above 120.
• What proportion of the population have an IQ below 80?
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Step 1: Sketch out question
-3 -2 -1 1 2 3
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Step 1: Sketch out question
-3 -2 -1 1 2 3
80
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Step 2: Calculate Z score
-3 -2 -1 1 2 3
80
(80 - 100) / 15 = -1.33
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Step 3: Look up Z score in Table
-3 -2 -1 1 2 3
80
Z = -1.33
.0918
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Example: IQ
• Mean IQ = 100
• SD = 15
• What proportion of the population have an IQ below 110?
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Step 1: Sketch out question
-3 -2 -1 1 2 3
![Page 81: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/81.jpg)
Step 1: Sketch out question
-3 -2 -1 1 2 3
110
![Page 82: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/82.jpg)
Step 2: Calculate Z score
-3 -2 -1 1 2 3
(110 - 100) / 15 = .67
110
![Page 83: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/83.jpg)
Step 3: Look up Z score in Table
-3 -2 -1 1 2 3
Z = .67
110
.7486
![Page 84: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/84.jpg)
Example: IQ
• A proportion of .7486 or 74.86 percent of the population have an IQ below 110.
![Page 85: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/85.jpg)
Finding the Proportion of the Population Between Two
Scores• What proportion of the population have IQ
scores between 90 and 110?
![Page 86: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/86.jpg)
Step 1: Sketch out question
-3 -2 -1 1 2 3
11090
?
![Page 87: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/87.jpg)
Step 2: Calculate Z scores for both values
• Z = (X - ) /
• Z = (90 - 100) / 15 = -.67
• Z = (110 - 100) / 15 = .67
![Page 88: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/88.jpg)
Step 3: Look up Z scores
-3 -2 -1 1 2 3
.67-.67
.2486 .2486
![Page 89: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/89.jpg)
Step 4: Add together the two values
-3 -2 -1 1 2 3
.67-.67
.4972
![Page 90: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/90.jpg)
• A proportion of .4972 or 49.72 percent of the population have an IQ between 90 and 110.
![Page 91: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/91.jpg)
• What proportion of the population have an IQ between 110 and 130?
![Page 92: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/92.jpg)
Step 1: Sketch out question
-3 -2 -1 1 2 3
110 130
?
![Page 93: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/93.jpg)
Step 2: Calculate Z scores for both values
• Z = (X - ) /
• Z = (110 - 100) / 15 = .67
• Z = (130 - 100) / 15 = 2.0
![Page 94: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/94.jpg)
Step 3: Look up Z score
-3 -2 -1 1 2 3
.67 2.0.4772
![Page 95: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/95.jpg)
Step 3: Look up Z score
-3 -2 -1 1 2 3
.67 2.0.4772
.2486
![Page 96: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/96.jpg)
Step 4: Subtract
-3 -2 -1 1 2 3
.67 2.0
.2286
.4772 - .2486 = .2286
![Page 97: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/97.jpg)
• A proportion of .2286 or 22.86 percent of the population have an IQ between 110 and 130.
![Page 98: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/98.jpg)
![Page 99: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/99.jpg)
Finding a score when given a probability
• IQ scores – what is the range of IQ scores we expect 95% of the population to fall?
• “If I draw a person at random from this population, 95% of the time his or her score will lie between ___ and ___”
• Mean = 100• SD = 15
![Page 100: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/100.jpg)
Step 1: Sketch out question
? 100 ?
95%
![Page 101: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/101.jpg)
Step 1: Sketch out question
? 100 ?
95% 2.5%2.5%
![Page 102: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/102.jpg)
Step 1: Sketch out question
? 100 ?
95% 2.5%2.5%
Z = 1.96Z = -1.96
![Page 103: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/103.jpg)
Step 3: Find the X score that goes with the Z score
• Z score = 1.96
• Z = (X - ) / • 1.96 = (X - 100) / 15
• Must solve for X
• X = + (z)()
• X = 100 + (1.96)(15)
![Page 104: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/104.jpg)
Step 3: Find the X score that goes with the Z score
• Z score = 1.96• Z = (X - ) / • 1.96 = (X - 100) / 15
• Must solve for X• X = + (z)()• X = 100 + (1.96)(15)• Upper IQ score = 129.4
![Page 105: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/105.jpg)
Step 3: Find the X score that goes with the Z score
• Must solve for X
• X = + (z)()
• X = 100 + (-1.96)(15)
• Lower IQ score = 70.6
![Page 106: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/106.jpg)
Step 1: Sketch out question
70.6 100 129.4
95% 2.5%2.5%
Z = 1.96Z = -1.96
![Page 107: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/107.jpg)
Finding a score when given a probability
• “If I draw a person at random from this population, 95% of the time his or her score will lie between 70.6 and 129.4”
![Page 108: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/108.jpg)
Practice
• GRE Score – what is the range of GRE scores we expect 90% of the population to fall?
• Mean = 500
• SD = 100
![Page 109: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/109.jpg)
Step 1: Sketch out question
? 500 ?
90% 5%5%
Z = 1.64Z = -1.64
![Page 110: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/110.jpg)
Step 3: Find the X score that goes with the Z score
• X = + (z)()• X = 500 + (1.64)(100)• Upper score = 664
• X = + (z)()• X = 500 + (-1.64)(100)• Lower score = 336
![Page 111: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/111.jpg)
Finding a score when given a probability
• “If I draw a person at random from this population, 90% of the time his or her score will lie between 336 and 664”
![Page 112: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/112.jpg)
Practice
![Page 113: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/113.jpg)
Practice
• The Neuroticism Measure
= 23.32
S = 6.24
n = 54
How many people likely have a neuroticism score between 18 and 26?
![Page 114: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/114.jpg)
Practice
• (18-23.32) /6.24 = -.85
• area = .3023
• ( 26-23.32)/6.26 = .43
• area = .1664
• .3023 + .1664 = .4687
• .4687*54 = 25.31 or 25 people
![Page 115: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/115.jpg)
Practice
• The Neuroticism Measure
= 23.32
S = 6.24
n = 54
How many people likely have a neuroticism score between 20 and 14?
![Page 116: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/116.jpg)
Practice
• (20-23.32) /6.24 = -.53
• area = .2019
• ( 14-23.32)/6.26 = -1.49
• area = .4319
• .4319-.2019 = .23
• .23*54 = 12.42 or 12 people
![Page 117: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/117.jpg)
Practice
• The Neuroticism Measure
= 23.32
S = 6.24
n = 54
How many people likely have a neuroticism score between 29 and 34?
![Page 118: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/118.jpg)
Practice
• (29-23.32) /6.24 = .91
• area = .3186
• ( 34-23.32)/6.26 = 1.71
• area =.4564
• .4564-.3186 = .1378
• .1378*54 = 7.44 or 7 people
![Page 119: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/119.jpg)
Practice
• On the next test I will give an A to the top 5 percent of this class.
• The average test grade is 56.82 with a SD of 6.98.
• How many points on the test did you need to get to get an A?
![Page 120: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/120.jpg)
Step 1: Sketch out question
.05
![Page 121: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/121.jpg)
Step 2: Look in Table Z
.05
Z score = 1.64
![Page 122: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/122.jpg)
Step 3: Find the X score that goes with the Z score
• Must solve for X
• X = + (z)()
• 68.26 = 56.82 + (1.64)(6.98)
![Page 123: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/123.jpg)
Step 3: Find the X score that goes with the Z score
• Must solve for X
• X = + (z)()
• 68.26 = 56.82 + (1.64)(6.98)
• Thus, a you need a score of 68.26 to get an A
![Page 124: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/124.jpg)
Practice
• The prestigious Whatsamatta U will only take people scoring in the top 97% on the verbal section SAT (i.e., they reject the bottom 3%).
• What is the lowest score you can get on the SAT and still get accepted?
• Mean = 500; SD = 100
![Page 125: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/125.jpg)
Step 1: Sketch out question
.03
![Page 126: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/126.jpg)
Step 2: Look in Table CZ score = -1.88
.03
![Page 127: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/127.jpg)
Step 3: Find the X score that goes with the Z score
• Must solve for X
• X = + (z)()
• 312 = 500 + (-1.88)(100)
![Page 128: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/128.jpg)
Step 3: Find the X score that goes with the Z score
• Must solve for X
• X = + (z)()
• 312 = 500 + (-1.88)(100)
• Thus, you need a score of 312 on the verbal SAT to get into this school
![Page 129: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/129.jpg)
![Page 130: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/130.jpg)
SPSS
PROGRAM:
https://citrixweb.villanova.edu/Citrix/MetaFrame/auth/welcome.htm
BASIC “HOW TO”
http://www.psychology.ilstu.edu/jccutti/138web/spss.html
SPSS “HELP” is also good
![Page 131: Practice](https://reader036.vdocument.in/reader036/viewer/2022062721/56813713550346895d9e9be2/html5/thumbnails/131.jpg)
SPSS PROBLEM #1
• Page 65• Data 2.1
• Turn in the SPSS output for
• 1) Mean, median, mode• 2) Standard deviation• 3) Frequency Distribution• 4) Histogram