The following table shows the information for a sample of 50 companies in the primary industry....

The following table shows the information for a sample of 50 companies in the primary
industry. The variable Sector indicates the sector in which the company is operating and
the variable Company size indicates the size of the company in terms of its annual turnover.
Sector Company size Sector Company size
1. Fishing Large 26. Fishing Medium
2. Fishing Medium 27. Fishing Large
3. Agriculture Medium    28. Fishing Medium
4. Fishing Large 29. Fishing Medium
5. Agriculture Medium 30. Agriculture Small
6. Fishing Large    31. Agriculture Large
7. Agriculture Small 32. Fishing Medium
8. Mining Large 33. Fishing Large
9. Mining Small 34. Fishing Large
10. Mining Large 35. Agriculture Medium
11. Agriculture Medium 36. Agriculture Large
12. Agriculture Medium 37. Agriculture Medium
13. Mining Large 38. Mining Large
14. Agriculture Small 39. Fishing Small
15. Fishing Medium    40. Agriculture Medium
16. Fishing Large    41. Mining Small
17. Agriculture Medium    42. Mining Medium
18. Fishing Medium 43. Agriculture Medium
19. Mining Medium    44. Mining Large
20. Fishing Medium 45. Fishing Large
21. Fishing Small 46. Mining Small
22. Mining Small    47. Mining Medium
23. Agriculture Small 48. Agriculture Medium
24. Mining Large 49. Mining Large
25. Agriculture Small 50. Mining Large

Use the information in the table above to answer the following questions.
a) For each of the two random variables, state whether it is a qualitative or
quantitative variable.
b) For each of the two random variables, state the scale of measurement.
c) Construct a cross tabulation table between Sector (rows) and Company size
(columns).
d) What is the probability that a randomly selected company is a large company?
e) What is the probability that a randomly selected company operate in the fishing
sector?
f) What is the probability that a randomly selected company is a medium size and it
operates in the agriculture sector?
g) What is the probability that a randomly selected company is either a small company
or a mining sector company or both?
h) What is the probability that a randomly selected company is either a small company
or a large company or both?
i) What is the probability that a randomly selected company is a small and large
company?
j) What is the probability that a randomly selected company is not a fishing sector
company?
k) What is the probability that a randomly selected company is not a medium size
company?
l) What is the probability that a randomly selected company is a mining sector
company if it is known that the company is a medium sized company?
m) If it is known that a company operate in the mining sector, what is the probability
that it is a medium size company?
n) Is company size statistically independent of sector in which the company operate?
Motivate.
o) If we define A = event company small and B = event company is large; are the events
A and B mutually exclusive? Motivate.

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