WGU C955 Formulas and Terms (Latest 2023/ 2024 Update) Applied Probability and Statistics | Questions and Verified Answers| 100% Correct

WGU C955 Formulas and Terms (Latest 2023/ 2024 Update) Applied Probability and Statistics | Questions and Verified Answers| 100% Correct

WGU C955 Formulas and Terms (Latest
2023/ 2024 Update) Applied Probability and
Statistics | Questions and Verified Answers|
100% Correct
Q: Simpsons Paradox
Answer:
A counterintuitive situation that occurs when a result that appears in individual groups of data
disappears or reverses when the groups are combined.
Can only occur when the sizes of the groups are inconsistent
Q: Lurking Variables :
Answer:

• A lurking variable is a variable not included in the study, but affects the variables that were
  included in the study• Never assume that a causation exists just because there is an association
  between two variables – always be on the lookout for lurking variables
  Q: Causation
  Answer:
  A change in one variable creates a change in the other variable.o
  Can only be determined from an experiment
  Q: Association
  Answer:
  means there is a relationship between two variables.Association does not necessarily imply
  causation.
  o We can use scatterplots to visualize the data and determine if there is at least an association, but
  we cannot determine causation from a scatterplot alone.o

Can establish association through an observational study.
Q: Observational Study
Answer:
There are no treatment or control groups because the participants self-select their groups.
Researchers observe if there is an association between variables.
Q: Experimental Study
Answer:

• Researchers randomly assign participants to two or more groups. One group is designated as a
  control group where no treatment (placebo) is given while all other groups are given treatments
  to determine if there is causation between variables.
  Q: Graphical Displays:
  Answer:
  Just C – Pie chart or bar chart• Just Q – Histogram, stem plot, boxplot, or dot plot•
  C ’ C – Two-way table with Conditional Percentages•
  C ’ Q – Side-by-side boxplot with 5-number summary• Q ’ Q – Scatterplot with correlation
  coefficient
  Q: Correlation Coefficient (Q ’ Q)
  Answer:
  Strength: On a scatterplot, the closer the points are laid out in a line,the stronger the correlation.
  measures the direction and strength of the linear relationship between the variables The closer r
  is to +1, the stronger the positive correlation. The closer r is to -1, the stronger the negative
  correlation. The closer r is to 0, the weaker the correlation.
  Q: Positive Correlation

Answer:
scatterplot reveals an “uphill trend.” as the explanatory variable increases, the response variable
increases.
Q: Negative Correlation
Answer:
scatterplot reveals a “downhill trend.”As the explanatory variable increases, the response
variable decreases.
Q: No CorrelationAnswer:
scatterplot reveals no trend between the variables
Q: Variable Type Q ’ Q
Answer:
Graphical Display: Scatterplot
Numerical Measure: Correlation Coefficient (r value)
Q: Variable Type C ’ Q
Answer:
Graphical Display: Side by Side Boxplots
Numerical Measure: Five Number Summary
Q: Variable Type C ’ C
Answer:
Graphical Display: Two Way Table
Numerical Measure: Conditional Percentages

Q: Explanatory Variable
Answer:
Influences the response variable.
Q: Response Variable
Answer:
Is affected by the explanatory variable.
Q: Standard Deviation Rule
Answer:
68% of the data is within 1 standard deviation of the mean.•
95% of the data is within 2 standard deviations of the mean.•
99.7% of the data is within 3 standard deviations of the mean
Q: Mode –
Answer:
value that occurs most often in a data set
Q: Median
Answer:
halfway point, equal number of data points above the median as below, always order the data
from smallest to largest first
Q: Mean
Powered by https://learnexams.com/search/study?query=

Open Circle
value is not included

Closed Circle
Value is included

1 Tbsp
3 tsp

1 fl oz
2 tbsp

1 L
1000 mL

1 kg
1000 g

1 g
1000 mg

m
slope

b
y-intercept

Positive slope
uphill line

Negative slope
downhill line

Quantitative (numerical) data
consists of data values that are numerical,
quantities that can be counted or measured (additions/subtractions make
sense)
Examples: Height, Salary, Chance of rain, Weigh

Categorical (qualitative) data
consist of data that are groups or labels,
and are not necessarily numerical (additions/subtractions do not make
sense)
Examples: Hair Color, Country of Origin, Blood Type, Zip Codes

Pie Chart
Displays parts of the whole, percentages

Bar Chart
Displays counts or frequencies of each category

Histogram
displays the shape and spread of data

Box Plot
displays center, spread and outliers. Each section covers 25%
of the data regardless of length. Can be horizontal or vertical

Dot Plot
displays clusters, gaps, and outliers for smaller data sets. Each
data value is seen in a dot plot

Stem Plot
Display shape according to place values. Each data value if
seen in a stem plot

Symmetric Normal
Mean, Median, and Mode are approximately equal.

Skewed Right (positively skewed)
Mode < Median < Mean.

Skewed left (negatively skewed)
Mean < Median < Mode.

Median
halfway point, equal number of data points above the
median as below, always order the data from smallest to largest firs

Explanatory Variable
Influences the response variable

Response Variable
Is affected by the explanatory variable

Experimental Study
Researchers randomly assign participants to
two or more groups. One group is designated as a control group
where no treatment (placebo) is given while all other groups are given
treatments to determine if there is causation between variables.

Observational Study
There are no treatment or control groups
because the participants self-select their groups. Researchers
observe if there is an association between variables

Association
means there is a relationship between two variables.
Association does not necessarily imply causation.

o We can use scatterplots to visualize the data and determine if
there is at least an association, but we cannot determine
causation from a scatterplot alone.
o Can establish association through an observational study

Causation
A change in one variable creates a change in the other
variable.

o Can only be determined from an experiment.

Lurking variable
A variable not included in the study, but affects
the variables that were included in the study. Never assume that a causation exists just because there is an
association between two variables – always be on the lookout for
lurking variables

Simpson’s Paradox
A counterintuitive situation that occurs when a result that appears in
individual groups of data disappears or reverses when the groups are
combined. Can only occur when the sizes of the groups are inconsistent.

Simple linear equation (regression line or line of best fit)
models
the data on a scatter plot with a line

o x is the explanatory variable, and y is the response variable
o Equation is given by y = mx + b where m is the slope and b is
the y-intercept

Sample Space
set of all possible outcomes.

Theoretical Probability =
Number of outcomes with the desired event/
Total number of outcomes

Tree Diagram
Used to determine the sample space

Complementary events
events that do not have any common
outcomes and when combined they comprise the sample space.
o P(not A) = 1 – P(A

P(A or B)
represents the probability that event A will occur, or
event B will occur, or both A and B will occur

P(A and B)
represents the probability that events A and B will
occur at the same time

P(A|B)
represents the probability that event A will occur, given
that event B has already occurred

Disjoint Events
cannot occur at the same time.
P(A and B) = 0
Example:

• A = Randomly selecting a person with type B blood.
• B = Randomly selecting a person with type O blood.

Independent Events
We say events A and B are
independent if the occurrence of one of them does not affect
the probability that the other will occur.
P(A|B) = P(A) and P(B|A) = P(B)

• “probability of A will be the same whether or not B
  has already occurred. Also, probability of B will be
  the same whether or not A has already occurred.”
  Example:
• A = Flipping a coin and landing on tails
• B = Rolling a die and landing on 3

OR Rule (General Addition)
P(A or B) = P(A) + P(B) – P(A and B)
Simplifies to P(A or B) = P(A) + P(B) for disjoint events

AND Rule (General Multiplication)
P(A and B) = P(A) x P(B|A)
Simplifies to P(A and B) = P(A) x P(B) for independent
events

Conditional Probability
P(B|A) = P(A and B)/
P(A)