MGMT 650-In a relative frequency contingency table, joint probabilities

Question 1
In a relative frequency contingency table, joint probabilities are located inside the margins.
For each row of joint probabilities, in the right margin and same row, sum the joint probabilities.
These are the row marginal probabilities. They are called marginal probabilities because they
are located in a margin of the table. For each column, in the bottom margin and same column,
sum the joint probabilities down the column. If the table has all the possible joint events, the
sum of all column marginal probabilities equals the sum of all row marginal probabilities equal 1.
Check that the sum of all column marginal probabilities equals the sum of all row marginal probabilities
equals 

1. Suppose we have different probabilities:
In favor
Democrat
Republican
Yes
0.15
0.20
No
0.25
0.40
Colum Total
0.40
0.60
P(yes and Republican) is a ______________ probability.
Conditional
Marginal
Joint Row total
0.35
0.65
1.00 Question 2
Suppose we know the following probabilities:
Republican
Democrat Independent
Totals
Female
0.148
0.153
0.044
0.345
Male
0.116
0.045
??
0.161
Totals
0.264
0.198
0.044
??
Enter the probability of events Democrat and Female occurring jointly with 3 decimal place accuracy: Question 3
Continuing with:
Male
Female Republican
0.611
0.126 P(male) is a __________probability.
Joint
Marginal
Conditional Democrat
0.003
0.125 Independent
0.048
0.088 Question 4
Suppose the probabilities have changed:
Republican
Democrat Independent
Totals
Female
0.188
0.022
0.021
0.231
Male
0.010
0.018
??
0.028
Totals
0.198
0.040
0.021
??
Compute the probability of the event Democrat, and enter your answer with 3 decimal places. Question 5
When the probability of event B is affected by the occurrence of event A, the events are not
independent. Let P(B|A) denote the probability of B given the condtion that A has occurred.
This is called a conditional probability.
*For independent events A and B, P(B|A)=P(B), and P(A|B)=P(A)
*For dependent events A and B:
P(B|A) ?P(B). The occurrence of A has changed the probability of B.
P(A|B) ?P(A). The occurrence of B has changed the probability of A.
For dependent events, P(A and B)= P(A) x P(B|A)=P(B) x P(A|B). This is the General Multiplication Rule.
Assume the following joint & marginal probabilities:
In favor
Democrat
Republican
Row Total
Yes
0.150
0.200
0.350
No
0.250
0.400
0.650
Column total
0.400
0.600
1.000
When we know the condition that some event has occurred, the table reduces to a row or column
matching the condition. For example, when we know that the party is Democrat, the table reduces to
the Democrat column:
In favor
Democrat
Yes
0.150
No
0.250
Column total
0.400
P(Yes|Democrat) is the probability of event Yes given the condition that the event Democrat has
occurred. In condition Democrat, Yes occurs at a rate of 0.15 in 0.40.
So P(Yes|democrat) = 0.15/0.40 = 0.375
P(Male|Republican) is a __________________probability.
Joint
Marginal
Conditional
Question 6
Given the following partial relative frequency table:
Republican
Democrat Independent Totals Male
0.159
0.167
0.156
Female
0.138
0.124
??
Totals
0.297
0.291
0.412
Compute P (Female|Democrat), and enter your answer with 3 decimal places. Question 7
Given the following partial relative frequencey table:
Republican
Democrat Independent
Male
0.196
0.165
0.196
Female
0.131
0.195
??
Totals
0.327
0.36
0.313
Compute P (Republican|male), and enter your answer with 3 decimal places. 0.482
0.262
?? Totals
0.557
0.326
?? Question 8
Assume breast cancer affects 0.003 of the female population between 45 and 55 years of age.
There are two kinds of positive test results:
* True positive (the test indicates you have a disease, and you actually have it).
* False positive (the test indicates you have a disease, but you do not have it).
Assume mammograms are:
*0.91 accurate detecting people who actually have breast can (true positive rate).
*0.90 accurate for people who do not have breast cancer (true negative rate).
Compute the probability that a female between the ages of 45 and 55 who tests
positive for breast cancer has breast cancer. Enter your answer with three decimal places. Question 9
We have a normal distribution with a mean of 72 and a standard deviation of 15. What is the Z value of
the value 74? Round to three decimal digits. Question 10
We have a normal distribution with a mean of 17 and a standard deviation of 3. What is the Z value
of the value 17? Round to three decimal digits. Question 11
In every normal distribution?
The interquartile range covers 68% of the values
The mean and the standard deviation are equal
The mean is larger than the standard deviation
The mean and the median are equal Question 12
In a normal distribution the probability of a value larger than one standard deviation about the mean is:
32%
16%
68%
There is not enough information to answer the question Question 13
The standard normal distribution is a normal distribution with the following characteristics:
The mean is 1 and the standard deviation is 0
The mean is 0 and the standard deviation is 1
The mean and standard deviation are 0
The mean and the standard deviation are 1