Practice
50
description
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Transcript of Practice
Practice
Stress Sense of Humor 4 2 10 8 12 11 5 3 7 8 6 7 2 3 14 13
A research was interested in the relation between stress and humor. Below are data from 8 subjects who completed tests of these two traits. Are these two variables related to each other? How much stress would a person probably experience if they had no sense of humor (i.e., score = 0)? How about if they had a high level of humor (i.e., score = 15)?
Practice
• r = .91
• Y = .77 + .98(Humor)
• .77 = .77 + .98(0)
• 15.47 = .77 + .98(15)
• You don’t want to have a sense of humor
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Ace 2 3 4 5 6 7 8 9 10 J Q K
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Ace 2 3 4 5 6 7 8 9 10 J Q K
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Fre
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cyWhat is the probability of picking an ace?
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Ace 2 3 4 5 6 7 8 9 10 J Q K
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Probability =
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Ace 2 3 4 5 6 7 8 9 10 J Q K
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Fre
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cyWhat is the probability of picking an ace?
4 / 52 = .077 or 7.7 chances in 100
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Ace
(.0
77)
2 (.
077)
3 (.
077)
4 (.
077)
5 (.
077)
6 (.
077)
7 (.
077)
8 (.
077)
9 (.
077)
10 (
.077
)
J (.
077)
Q (
.077
)
K (
.077
)
Card
Fre
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cyEvery card has the same probability of being picked
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Ace
(.0
77)
2 (.
077)
3 (.
077)
4 (.
077)
5 (.
077)
6 (.
077)
7 (.
077)
8 (.
077)
9 (.
077)
10 (
.077
)
J (.
077)
Q (
.077
)
K (
.077
)
Card
Fre
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cyWhat is the probability of getting a 10, J, Q, or K?
0
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Ace
(.0
77)
2 (.
077)
3 (.
077)
4 (.
077)
5 (.
077)
6 (.
077)
7 (.
077)
8 (.
077)
9 (.
077)
10 (
.077
)
J (.
077)
Q (
.077
)
K (
.077
)
Card
Fre
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cy(.077) + (.077) + (.077) + (.077) = .308
16 / 52 = .308
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Ace
(.0
77)
2 (.
077)
3 (.
077)
4 (.
077)
5 (.
077)
6 (.
077)
7 (.
077)
8 (.
077)
9 (.
077)
10 (
.077
)
J (.
077)
Q (
.077
)
K (
.077
)
Card
Fre
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cyWhat is the probability of getting a 2 and then after replacing the card getting a 3 ?
0
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Ace
(.0
77)
2 (.
077)
3 (.
077)
4 (.
077)
5 (.
077)
6 (.
077)
7 (.
077)
8 (.
077)
9 (.
077)
10 (
.077
)
J (.
077)
Q (
.077
)
K (
.077
)
Card
Fre
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cy(.077) * (.077) = .0059
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Ace
(.0
77)
2 (.
077)
3 (.
077)
4 (.
077)
5 (.
077)
6 (.
077)
7 (.
077)
8 (.
077)
9 (.
077)
10 (
.077
)
J (.
077)
Q (
.077
)
K (
.077
)
Card
Fre
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cyWhat is the probability that the two cards you draw will be a black jack?
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Ace
(.0
77)
2 (.
077)
3 (.
077)
4 (.
077)
5 (.
077)
6 (.
077)
7 (.
077)
8 (.
077)
9 (.
077)
10 (
.077
)
J (.
077)
Q (
.077
)
K (
.077
)
Card
Fre
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cy10 Card = (.077) + (.077) + (.077) + (.077) = .308
Ace after one card is removed = 4/51 = .078
(.308)*(.078) = .024
Practice
• What is the probability of rolling a “1” using a six sided dice?
• What is the probability of rolling either a “1” or a “2” with a six sided dice?
• What is the probability of rolling two “1’s” using two six sided dice?
Practice
• What is the probability of rolling a “1” using a six sided dice?1 / 6 = .166
• What is the probability of rolling either a “1” or a “2” with a six sided dice?
• What is the probability of rolling two “1’s” using two six sided dice?
Practice
• What is the probability of rolling a “1” using a six sided dice?1 / 6 = .166
• What is the probability of rolling either a “1” or a “2” with a six sided dice?(.166) + (.166) = .332
• What is the probability of rolling two “1’s” using two six sided dice?
Practice
• What is the probability of rolling a “1” using a six sided dice?1 / 6 = .166
• What is the probability of rolling either a “1” or a “2” with a six sided dice?(.166) + (.166) = .332
• What is the probability of rolling two “1’s” using two six sided dice?(.166)(.166) = .028
Next step
• Is it possible to apply probabilities to a normal distribution?
Theoretical Normal Curve
-3 -2 -1 1 2 3
Theoretical Normal Curve
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
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
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
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
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
These values are given in Table C on page 390
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.3413 .3413
.1587 .1587
To use this table look for the Z score in column AColumn B is the area between that score and the mean
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.3413 .3413
.1587 .1587
Column B
To use this table look for the Z score in column AColumn C is the area beyond the Z score
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.3413 .3413
.1587 .1587
Column C
The curve is symmetrical -- so the answer for a positive Z score is the same for a negative Z score
-3 -2 -1 1 2 3
Z-scores -3 -2 -1 0 1 2 3
.3413 .3413
.1587 .1587
Column C
Column B
Practice
• What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
• Between mean and z = .56?
• Beyond z = 2.25?
• Between the mean and z = -1.45
Practice
• What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
• Between mean and z = .56?.2123
• Beyond z = 2.25?
• Between the mean and z = -1.45
Practice
• What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
• Between mean and z = .56?.2123
• Beyond z = 2.25?.0122
• Between the mean and z = -1.45
Practice
• What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
• Between mean and z = .56?.2123
• Beyond z = 2.25?.0122
• Between the mean and z = -1.45.4265
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
Note• This is using a hypothetical distribution
• Due to chance, empirical distributions are not always identical to theoretical distributions
• If you sampled an infinite number of times they would be equal!
• The theoretical curve represents the “best estimate” of The theoretical curve represents the “best estimate” of how the events would actually occurhow the events would actually occur
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cyEmpirical Distribution based on 52 draws
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Theoretical Normal Curve
Empirical Distribution
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
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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
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t
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0
Empirical Distribution
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
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t40
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0
Empirical Distribution
PROGRAM
http://www.jcu.edu/math/isep/Quincunx/Quincunx.html
Theoretical Normal Curve
Normality frequently occurs in many situations of psychology, and other sciences
Practice
– #7.7
– #7.8
