1) According to the local union president, the mean gross income of plumbers in the Salt Lake area follows the normal probability distribution with a mean of $45,000 and a population standard deviation of $3,000. A recent investigative reporter for KYAK TV found, for a sample of 120 plumbers, the mean gross income was $45,500. At the .10 significance level, is it reasonable to conclude that the mean income is not equal to $45,000? Determine the p-value.

2) Jane has just begun her new job as on the sales force of a very competitive company. In a sample of 16 sales calls it was found that she closed the contract for an average value of 108 dollars with a standard deviation of 12 dollars. Test at 5% significance that the population mean is at least 100 dollars against the alternative that it is less than 100 dollars. Company policy requires that new members of the sales force must exceed an average of $100 per contract during the trial employment period. Can we conclude that Jane has met this requirement at the significance level of 95%?

3) According to the Us bureau of labor statistics the following are the averages for manufacturing industry in the U.S.

Average Annual Pay roll $3,250 ,000

Average number of employees is 64,000

A candidate for government office claims that the Average payroll and average number of employees is actually less than what was claimed in the bureau report. They are using this claim as a incentive to push certain tax incentive laws for manufacturing industry. The candidate samples 199 manufacturing sectors

Use the Manufacturing hypothesis test excel data( DATA SET MODULE) to perform a hypothesis test to the candidates claim

a) test the average annual pay roll 0.05 significance level

State the null and alternate hypothesis

State the conclusion of your test in a complete sentence using the context of the problem

b) test average number of employees at the 0.05 significance level

State the null and alternate hypothesis

State the conclusion of your test in a complete sentence using the context of the problem