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.
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 _ _ $30,000 and compute the p-value.
c. With α _ .05 as the level of significance, what is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.