##### Reference no: EM1311606

Wall Street securities firms paid out record year-end bonuses of $125,500 per employee for 2005 (*Fortune*, February 6, 2006). Suppose we would like to take a sample of employees at the Jones & Ryan securities firm to see whether the mean year-end bonus is different from the reported mean of $125,500 for the population.

a. State the null and alternative hypotheses you would use to test whether the year-end bonuses paid by Jones & Ryan were different from the population mean.

H_{0}: µ =

H_{a}: µ =

b. Suppose a sample of 40 Jones & Ryan employees showed a sample mean year-end bonus of $118,000. Assume a population standard deviation of $33,000 and compute the p-value (to 4 decimals).

c. With α = .05 as the level of significance, what is your conclusion?

Answer the next three questions using the critical value approach.

d. Using α = .05, what is the critical value for the test statistic? (+ or -)

e. Calculate the test statistic (to 2 decimals).

f. Using α = .05, can you conclude that the year-end bonuses paid by Jones & Ryan were different from the population mean?