A survey conducted by the Segal Company of New York found that in a sample of 18

Question

A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their non-cash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members.

1) Set up a contingency table.

2) Referring to the table, if a company is selected at random, what is the probability that the company is small to mid-sized and did not offer stock options to their board members?

3) Referring to The table, if a company is selected at random, what is the probability that the company is small to mid-sized or offered stock options to their board members?

4) Referring to the table, if a randomly selected company is a large company, what is the probability that it offered stock options to their board members?

5) Referring to the table, if a randomly selected company offered stock options to their board members, what is the probability that it is a large company?

6) Referring to The table, is the size of the company independent of whether stock options are offered to their board members and why?

Explanation / Answer

1) Contingency Table

2) Probability that the company is small to mid-sized and did not offer stock options to their board members =

=137/369 = 0.3713

3) Probability that the company is small to mid-sized or offered stock options to their board members

= (180+83-43)/369 = 220/369 = 0.5962

4) Probability that it offered stock options to their board members = 83/369 = 0.2249

5)  Probability that it is a large company = 40/83 = 0.4819

6) No, because P(stock option) is not equal to P(stock option | large)

Comany Size Total Large Small to mid sized Stock Options Yes 40 43 83 No 149 137 286 Total 189 180 369

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