Fortune magazine reported the results of a survey on executi

Fortune magazine reported the results of a survey on executive training that was conducted by the Association of Executive Search Consultants. The survey showed that 75 percent of 300 polled CEOs believe that companies should have “fast-track training programs” for developing managerial talent.

Based on the probability you computed in part a, would you conclude that more than 70 percent of CEOs believe that companies should have fast-track training programs?

Solution

(a) Suppose we wish to use the results of this survey to justify the claim that more than 70 percent of CEOs believe that companies should have fast-track training programs. Assuming that the 300 surveyed CEOs were randomly selected, and assuming, for the sake of argument, that 70 percent of CEOs believe that companies should have fast-track training programs (that is, p = .70), calculate the probability of observing a sample proportion of .75 or more. That is, calculate P( > .75). (Round your answer to µ to 2 decimal places. Round your final answers to 4 decimal places. Do not round the intermediate calculations.)

n=300 p = .70

sd = sqrt(p(1-p)/300)=sqrt(0.7*0.3/300) =0.0265

z value for 0.75, z=(0.75-0.70).0.0265 =1.89

P( p>0.75)= P( z>1.89)

=0.0294

(b) Based on the probability you computed in part a, would you conclude that more than 70 percent of CEOs believe that companies should have fast-track training programs?

Yes

Yes, Calculated probability p=0.0294 which is less than 0.05.