Question

In: Statistics and Probability

2. Use the table below to answer the following questions. Increase Use of Business Focus Linkedin...

2. Use the table below to answer the following questions.

Increase Use of

Business Focus

Linkedin

B2B

B2C

Total

YES

1478

_______

1027

_______

2505

_______

NO

467

_______

841

_______

1308

_______

Total

1945

_______

1868

_______

3813

_______

  1. Calculate the joint and marginal probabilities for the data above. Fill in the probability for each cell on the line above. Round to three decimal places. (3 points)
  1. What is the marginal probability of Yes increased Use of Linkedin (Yes)? Round to three decimal places. (1 point)

  1. What is the conditional probability that Yes increased use of Lindedin given a B2C business focus [P(YES | B2C)]? Round to three decimal places. (1 point)
  1. Are Increase use of Linkedin and Business Focus independent? (1 point)

Solutions

Expert Solution

Solution:

Given:

Increase Use of

Business Focus

Linkedin

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

Linkedin

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

Linkedin

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.


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