SOLUTION: The following table shows gender and soda preference of 300 people sampled: Soda Preference Gender Diet Soda Regular Soda No Soda Totals Male 70 40 20 130 Fe

Question 126318: The following table shows gender and soda preference of 300 people sampled:

Soda Preference
Gender Diet Soda Regular Soda No Soda Totals
Male 70 40 20 130
Female 110 45 15 170
Total 180 85 35 300
A. Draw a Bayesian Tree from the data in the table.
B. Are these two variables (gender & soda preference) independent?
C. What is the probability of randomly selecting someone who is Male or prefers Regular Soda?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Soda Preference
Gender Diet Soda Regular Soda No Soda Totals
Male 70 40 20 130
Female 110 45 15 170
Total 180 85 35 300
A. Draw a Bayesian Tree from the data in the table.
The tree has two roots: Male and Female
Each root as three brances: Diet, Regular, None
Read the probabilities of the branches from the data
For example the branch Male-Diet has probability (70/130)= 7/13
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B. Are these two variables (gender & soda preference) independent?
Ho: The rows are independent
Ha: The rows are dependent
Chi-square Test:
Chi-Square = 29.179441
p-value = 4.61x10^-7 or extremely small
Conclusion: Fail to reject Ho
The gender and soda preference are independent.
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C. What is the probability of randomly selecting someone who is Male or prefers Regular Soda?
P(Male or prefers Regular) = P(M)+P(R)-P(M and R)
= 130/300 + 85/300 - 40/300 = 175/300
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Cheers,
Stan H.

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