Imagine that you are a future CEO of Trojan Worldwide and are interested in the average age and average 1-year compensation of the highest paid CEO's in the annual Forbes list. You decide to contact an expensiveexclusive CEO placement service company. They provide you with a sample of 50 CEOs, their compensation and age. So you decide to study the information given to you. Treat the CEO information from theExecutive_Compensation_Forbes2020data_population.jmpas the population and 50 randomly selected CEO provided by the CEO placement service as the sample.

Use the sample information for the calculations-Data from

SubsetofExecutive_Compensation_Forbes2020data_sample.jmp-Note: I have given all the required printouts.

Answer the following questions,

1) Obtain the 95% confidence interval for the mean 1-Year compensation and mean age. Does your confidence interval contain the population mean 1-Year compensation and population mean age? Explain the 95% confidence intervals obtained in simple English. Do they make business sense?

2) Find the probability that the average compensation for the 50 randomly selected CEOs is more than the sample mean; under the assumption the true mean is8 million dollars.

(Hint: Use the sample standard deviation as an approximation for the population standard deviation and use Z-table to find the probability)

3) The exclusive CEO placement service claims that the average compensation for CEO placed by their services is more than 8 million dollars. Assuming the sample given is obtained from the placement services; does the sample support the placement services claim? Test the hypothesis at 5% Level and state your conclusion. Is your p-value close to the answer obtained in part (b), explain.

The extreme value(s) have affected your above calculations and you decide to drop them. You decide to drop the top 3 extreme values from your calculation. (SubsetofExecutive_Compensation_Forbes2020data_sample.jmphas the data sorted according to 1-Year compensation)

4) Obtain the 95% confidence interval for the mean 1-Year compensation and mean age. Does your confidence interval contain the population mean 1-Year compensation and population mean age? Explain the 95% confidence intervals obtained in simple English. Does it make business sense? (JMP: Print the 95% confidence Interval for mean compensation and mean age.)

5) Redo the hypothesis test and state your conclusions. Does your conclusion change, why or why not?