A
contingency table provides a way of portraying data that can facilitate calculating probabilities. The table helps in determining conditional probabilities quite easily. The table displays sample values in relation to two different variables that may be dependent or contingent on one another. Later on, we will use contingency tables again, but in another manner.
Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data:
Speeding violation in the last year
No speeding violation in the last year
Total
Cell phone user
25
280
305
Not a cell phone user
45
405
450
Total
70
685
755
The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and 685. Notice that 305 + 450 = 755 and 70 + 685 = 755.
Calculate the following probabilities using the table.
a. Find
P (Person is a car phone user).
a.
b. Find
P (person had no violation in the last year).
b.
c. Find
P (Person had no violation in the last year
was a car phone user).
c.
d. Find
P (Person is a car phone user
person had no violation in the last year).
d.
e. Find
P (Person is a car phone user
person had a violation in the last year).
e.
(The sample space is reduced to the number of persons who had a violation.)
f. Find
P (Person had no violation last year
person was not a car phone user)
f.
(The sample space is reduced to the number of persons who were not car phone users.)
Try it
[link] shows the number of athletes who stretch before exercising and how many had injuries within the past year.
Injury in last year
No injury in last year
Total
Stretches
55
295
350
Does not stretch
231
219
450
Total
286
514
800
What is
P (athlete stretches before exercising)?
What is
P (athlete stretches before exercising
no injury in the last year)?
P (athlete stretches before exercising) =
= 0.4375
P (athlete stretches before exercising
no injury in the last year) =
= 0.5739
[link] shows a random sample of 100 hikers and the areas of hiking they prefer.
Hiking area preference
Sex
The Coastline
Near Lakes and Streams
On Mountain Peaks
Total
Female
18
16
___
45
Male
___
___
14
55
Total
___
41
___
___
a. Complete the table.
a.
Hiking area preference
Sex
The Coastline
Near Lakes and Streams
On Mountain Peaks
Total
Female
18
16
11
45
Male
16
25
14
55
Total
34
41
25
100
b. Are the events "being female" and "preferring the coastline" independent events?
Let
F = being female and let
C = preferring the coastline.
Find
.
Find
P (
F )
P (
C )
Are these two numbers the same? If they are, then
F and
C are independent. If they are not, then
F and
C are not independent.
b.
= 0.18
P (
F )
P (
C ) =
= (0.45)(0.34) = 0.153
≠
P (
F )
P (
C ), so the events
F and
C are not independent.
c. Find the probability that a person is male given that the person prefers hiking near lakes and streams. Let
M = being male, and let
L = prefers hiking near lakes and streams.
What word tells you this is a conditional?
Fill in the blanks and calculate the probability:
P (___
___) = ___.
Is the sample space for this problem all 100 hikers? If not, what is it?
c.
The word 'given' tells you that this is a conditional.
P (
ML ) =
No, the sample space for this problem is the 41 hikers who prefer lakes and streams.
d. Find the probability that a person is female or prefers hiking on mountain peaks. Let
F = being female, and let
P = prefers mountain peaks.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
