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The Bureau of Labor Statistics reported that the average yearly income of executives in the year 2005 was $110,000. A sample of 81 executives, which was taken in 2006, showed an average yearly income of $120,000.

a. We want to test to determine if there has been a significant increase in the average yearly income of executives. Develop the null and alternative hypothesis for this problem.
b. Test this problem at 99% confidence and provide conclusion.
c. Would the problem have a similar conclusion if we knew the population standard deviation was $40,000? Why?

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