Question

) ABC Securities Firm paid out record year-end bonuses of $150,000 per employee for 2005. Suppose we would like to take a sample of employees at the ABC Securities firm to see whether the mean year-end bonus is different from the reported mean of $150,000 for the population. a) State the null and alternative hypotheses you would use to test whether the year-end bonuses paid by ABC Securities were different from the population mean. b) Suppose a sample of 40 employees showed a sample mean year-end bonus of $130,000. Assume a population standard deviation of $30,000 and compute the p- value. c) With a .05 as the level of significance, what is your conclusion? d) Repeat the preceding hypothesis test using the critical value approach.

Please use excel.

Answer 1

a) The Hypotheses are:

given that n=40 and Population standard deviation, =30000

and Sample mean =130000

Rejection region:

Reject Ho if |Z_obs|>Z_0.025=1.96 and P-value < =0.05

Test statistic:

P value:

P value associated with the Z score calculated using the Z table or by the calculator, the table is shown below.

Conclusion:

Since|Z_obs|>Z_0.025 and P value <<0.05 hence we reject the null hypothesis and conclude that there is enough evidence to support that the mean year-end bonus is different from the reported mean of $150,000 for the population.

P value =0.00004