### Null-alternative hypotheses

Assignment Help Basic Statistics
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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.

H0: µ =

Ha: 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?

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