In: Statistics and Probability
2. Use the table below to answer the following questions.
Increase Use of |
Business Focus |
||
|
B2B |
B2C |
Total |
YES |
1478 _______ |
1027 _______ |
2505 _______ |
NO |
467 _______ |
841 _______ |
1308 _______ |
Total |
1945 _______ |
1868 _______ |
3813 _______ |
Solution:
Given:
Increase Use of |
Business Focus |
||
|
B2B |
B2C |
Total |
YES |
1478 _______ |
1027 _______ |
2505 _______ |
NO |
467 _______ |
841 _______ |
1308 _______ |
Total |
1945 _______ |
1868 _______ |
3813 _______ |
Part a) Calculate the joint and marginal probabilities for the data above.
To find joint probabilities , divide each cell frequency by Total 3813 and to find marginal probabilities divide each row total and each column total by total 3813
Thus we get:
Increase Use of |
Business Focus |
||
|
B2B |
B2C |
Total |
YES |
1478 1478/3813 |
1027 1027/3813 |
2505 2505/3813 |
NO |
467 467/3813 |
841 841/3813 |
1308 1308/3813 |
Total |
1945 1945/3813 |
1868 1868/3813 |
3813 3813/3813 |
Thus joint and marginal probabilities are:
Increase Use of |
Business Focus |
||
|
B2B |
B2C |
Total |
YES |
1478 0.388 ______ |
1027 0.269 _____ |
2505 0.657 _____ |
NO |
467 0.122 _____ |
841 0.221 ______ |
1308 0.343 ______ |
Total |
1945 0.510 _____ |
1868 0.490 _____ |
3813 1.000 ______ |
Part b) What is the marginal probability of Yes increased Use of Linkedin (Yes)?
P(Yes) = .........?
P(Yes) = 0.657
Part c) What is the conditional probability that Yes increased use of Lindedin given a B2C business focus [P(YES | B2C)]?
P(YES | B2C) =..............?
P(YES | B2C) = P( YES and B2C) / P(B2C)
P(YES | B2C) = 0.269 / 0.490
P(YES | B2C) = 0.549
Part d) Are Increase use of Linkedin and Business Focus independent?
P(YES | B2C) = 0.549 and P(YES) = 0.657
Since P(YES | B2C)= 0.549 which is not equal to P(YES)= 0.657, thus increase use of Linkedin and Business Focus are NOT independent.