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The Bureau of Labor Statistics reported that the average annual income of dentists in the year 2005 was $110,000. A sample of 81 dentists, which was taken in 2006, showed an average annual income of $115,000. Assume the standard deviation of the population of dentists in 2006 is $36,000.

a). Suppose you want to test whether there has been a significant increase in the average annual income of the dentists. List your null and alternative hypotheses below:

b). Calculate the test statistic, determine the p-value, and at α = 0.05 significance level, test the hypotheses and draw your conclusion. [You MUST use the p-value approach.]

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