Question

5) 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

Answer 1

a) H₀: = 150000

H1: 150000

b) The test statistic z = ()/()

= (130000 - 150000)/(30000/)

= -4.22

P-value = 2 * P(Z < -4.22)

= 2 * 0 = 0

C) Since the p-value is less than the significance level (0 < 0.05), so we should reject the null hypothesis.

At 0.05 significance level, we can conclude that the year-end bonus of paid by ABC securities were different from the population mean.

d) At 0.05 significance level the critical values are +/- z_0.025 = +/- 1.96

Since the test statistic value is less than the negative critical value(-4.22 < -1.96), so we should reject the null hypothesis.

At 0.05 significance level, we can conclude that the year-end bonus of paid by ABC securities were different from the population mean.