Sample Space Shopper type Shop Not Shop T otals Social attitudes Social 320 80 4
ID: 2814667 • Letter: S
Question
Sample Space
Shopper type
Shop
Not Shop
T otals
Social attitudes
Social
320
80
400
Not Social
160
40
200
T otals
480
120
600
Sample Space
Shopper type
Shop
Not Shop
T otals
Social attitudes
Social
375
0
375
Not Social
125
100
225
T otals
500
100
600
Sample Space
Shopper type
Shop
Not Shop
T otals
Social attitudes
Social
300
150
450
Not Social
100
50
150
T otals
400
200
600
this question for QUANTITATIVE METHODS FOR BUSINESS
Managerial Decision III: Analysing Socializer Shopping Traffic To help you understand the long-term potential of offering products for sale on Socializer in Australia, The US and Japan, you decide to obtain online users views on their likely purchasing habits of visitors to a well know internet site during March 2010, broken down by each country. You wish to predict the probability of people using the Socializer site to purchase items from SalesGalore!s. Six hundred users in each country were surveyed to determine whether a person who uses an online social networking facility (labeled social attitudes) would also purchase a product (labeled shopper type) through that facility. For each country answer the questions that follow. In each case show the both the full probability statement and all supporting calculations. Australia USA Japan Required:
(a) (6 marks) What is the probability that a person uses a social networking site?
(b) (6 marks) What is the probability that a person will shop online?
(c) (6 marks) What is the probability that a person will not use a social networking site and they shop online?
(d) (6 marks) Suppose a person who uses a social networking site. What is then the probability that they will shop online?
(e) (6 marks) Suppose that a person shops online. What is then the probability that this person will not use a social networking site?
(f) (12 marks) Are ‘social attitudes’ and ‘shopper type’ independent or dependent? How do you know? Show calculations that support your answer.
Note: In order to achieve full marks for this question it is essential that you fully explain what you are doing, why you are doing it and the steps involved in providing a final solution. Ensure your answer is not just a set of calculations as 25% of the marks for this question are set aside for your explanation.
Sample Space
Shopper type
Shop
Not Shop
T otals
Social attitudes
Social
320
80
400
Not Social
160
40
200
T otals
480
120
600
Explanation / Answer
a) Total number of persons in Australia, USA, and Japan = 600 x 3 = 1800
Total number of social persons in Australia = 320 + 80 = 400
Total number of social persons in USA = 375 + 0 = 375
Total number of social persons in Japan = 300 + 150 = 450
Total number of social persons in Australia, USA, and Japan = 400 + 375 +450 = 1225
So, probability that a person uses a social networking site
= Total number of social persons in Australia, USA, and Japan / Total number of persons in Australia, USA, and Japan
= 1225 / 1800
= 0.681
b) Total number of persons in Australia, USA, and Japan = 600 x 3 = 1800
Total number of social persons who shops in Australia = 320 = 480
Total number of social persons who shops in USA = 375 + 125 = 500
Total number of social persons who shops in Japan = 300 + 100 = 400
Total number of social persons who shops in Australia, USA, and Japan = 320 + 375 +300 = 995
So, probability that a person will shop online:
= Total number of social persons who shops in Australia, USA, and Japan / Total number of persons in Australia, USA, and Japan
= 1380 / 1800
= 0.77
c) Total number of persons in Australia, USA, and Japan = 600 x 3 = 1800
Total number of persons will not use a social networking site and they shop online in Australia = 160
Total number of persons will not use a social networking site and they shop online in USA = 125
Total number of persons will not use a social networking site and they shop online in Japan = 100
Total number of persons will not use a social networking site and they shop online in Australia, USA, and Japan = 160 + 125 + 100 = 385
So, probability that a person will not use a social networking site and they shop online
= Total number of persons who will not use a social networking site and they shop online in Australia, USA, and Japan / Total number of persons in Australia, USA, and Japan
= 385 / 1800
= 0.214
d) Total number of persons in Australia, USA, and Japan = 600 x 3 = 1800
Total number of persons who will use a social networking site and they shop online in Australia = 320
Total number of persons who will use a social networking site and they shop online in USA = 375
Total number of persons who will use a social networking site and they shop online in Japan = 300
Total number of persons who will use a social networking site and they shop online in Australia, USA, and Japan = 320 + 375 + 300 = 995
So, probability that a person will use a social networking site and they shop online
= Total number of persons who will use a social networking site and they shop online in Australia, USA, and Japan / Total number of persons in Australia, USA, and Japan
= 995 / 1800
= 0.553
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