To evaluate the statistical relationship between the profitability of firms and the educational qualifications of their CEOs, a simple random sample of 118 firms was collected and data on the following two variables obtained:

Profiti= Annual profit of firmiin millions of dollars

Gradi= 1 if the CEO of firmihad a post-graduate degree, = 0 otherwise.

The sample mean of the observations forProfitiwas calculated to be 0.184 ($million), with standard deviation of 0.326. There were 68 CEOs in the sample who had a post-graduate degree. The sample covariance betweenProfitiandGradiwas 0.028.

1. (1 mark) What is thesample meanofGradi?
2. (2 marks) Thesample varianceofGradiwas calculated to be 0.246. Briefly explain how this was calculated using only the information given in this question.
3. (3 marks) Calculate a 95% confidence interval for the proportion of firms whose CEOs have a post-graduate degree. (Report your standard error and critical value as well as the confidence interval itself.)
4. (2 marks) Consider a regression of the form
5. E(Profiti|Gradi) = 0+ 1Gradi
6. Use the provided sample statistics to calculate 0and 1.
7. (2 marks) Use your regression results to calculate the sample mean of profits for firms whose CEOs do not have a post-graduate degrees. Explain how you did the calculation.
8. (2 marks) Use your regression results to calculate the sample mean of profits for firms whose CEOs do have a post-graduate degree. Explain how you did the calculation.