Contingency Tables and Probability Trees Quiz
The question sheet
Reveal any answer as you study-
What does a contingency table display?
- Values for two variables
- Only totals
- Continuous curves
- A single random variable
Reveal answer
Answer: Values for two variables
Source evidence
PDF page 159: 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.
-
In the cell phone study, what is the total number of people in the sample?
- 755
- 450
- 685
- 305
Reveal answer
Answer: 755
Source evidence
PDF page 160: The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and
PDF page 160: Speeding violation in the No speeding violation in the Total last year last year Uses cell phone while driving 25 280 305 Does not use cell phone while 45 405 450 driving Total 70 685 755
-
What is P(Driver is a cell phone user)?
- 280/755
- 70/755
- 685/755
- 305/755
Reveal answer
Answer: 305/755
Source evidence
PDF page 160: Solution 3.20 number of cell phone users 305 a. = total number in study 755
-
What is P(Driver had no violation in the last year)?
- 685/755
- 70/755
- 450/755
- 305/755
Reveal answer
Answer: 685/755
Source evidence
PDF page 160: Solution 3.20 number that had no violation 685 b. = total number in study 755
-
What is P(cell phone user | had a violation last year)?
- 25/70
- 25/305
- 70/755
- 280/305
Reveal answer
Answer: 25/70
Source evidence
PDF page 160: Solution 3.20 25 e. (The sample space is reduced to the number of drivers who had a violation.) 70
-
For P(no violation | not a cell phone user), the sample space reduces to what?
- Number who were not cell phone users
- All 755 drivers
- Number with violations
- Number of cell phone users
Reveal answer
Answer: Number who were not cell phone users
Source evidence
PDF page 161: Solution 3.20 405 f. (The sample space is reduced to the number of drivers who were not cell phone users.) 450
-
In the hiking table, how many females were sampled in total?
- 55
- 34
- 100
- 45
Reveal answer
Answer: 45
Source evidence
PDF page 161: Female 18 16 11 45 Male 16 25 14 55 Total 34 41 25 100
-
Why are 'being female' and 'preferring coastline' not independent?
- Both equal zero
- They are mutually exclusive
- P(F∩C) ≠ P(F)P(C)
- P(F∩C) equals P(F)P(C)
Reveal answer
Answer: P(F∩C) ≠ P(F)P(C)
Source evidence
PDF page 162: ⎝100⎠⎝100⎠ P(F ∩ C) ≠ P(F)P(C), so the events F and C are not independent.
-
In the hiking study, P(F∩C) equals which value?
- 0.34
- 0.153
- 0.18
- 0.45
Reveal answer
Answer: 0.18
Source evidence
PDF page 162: Solution 3.21 b. ⎛ ⎞ 18
PDF page 162: = 0.18 ⎝ ⎠ 100 ⎛ 45 ⎞⎛ 34 ⎞
-
What is P(F)P(C) in the hiking independence check?
- 0.153
- 0.34
- 0.45
- 0.18
Reveal answer
Answer: 0.153
Source evidence
PDF page 162: = (0.45)(0.34) = 0.153
-
What is a tree diagram used to determine?
- A single probability only
- The outcomes of an experiment
- The mean of data
- The variance
Reveal answer
Answer: The outcomes of an experiment
Source evidence
PDF page 165: Sometimes, when the probability problems are complex, it can be helpful to graph the situation. Tree diagrams can be used to visualize and solve conditional probabilities. Tree Diagrams A tree diagram is a special type of graph used to determine the outcomes of an experiment. It consists of "branches" that are labeled with either frequencies or probabilities. Tree diagrams can make some probability problems easier to visualize and solve. The following example illustrates how to use a tree diagram.
-
For the 11-ball urn drawn with replacement, how many total outcomes are there?
- 24
- 64
- 121
- 110
Reveal answer
Answer: 121
Source evidence
PDF page 166: The first set of branches represents the first draw. The second set of branches represents the second draw. Each of the outcomes is distinct. In fact, we can list each red ball as R1, R2, and R3 and each blue ball as B1, B2, B3, B4, B5, B6, B7, and B8. Then the nine RR outcomes can be written as: R1R1; R1R2; R1R3; R2R1; R2R2; R2R3; R3R1; R3R2; R3R3 The other outcomes are similar. There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.
PDF page 166: Figure 3.2 Total = 64 + 24 + 24 + 9 = 121
Introductory Business Statistics
Introductory Business Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
Make your own — free
Turn any notes into a game in under a minute. Free to start.