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 _______

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)

What is the marginal probability of Yes increased Use of Linkedin (Yes)? Round to three decimal places. (1 point)

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)

Are Increase use of Linkedin and Business Focus independent? (1 point)

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.

orchestra answered 2 years ago

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