Question

Bay Street securities firms paid out record year-end bonuses of $130,500 per employee for 2014. Suppose we would like to take a sample of employees at the Roy-West securities firm to see whether the mean year-end bonus is greater than the reported mean of $130,500 for the population. (a)State the null and alternative hypothesis you would use to test whether the year end bonuses paid by Roy-West where greater than the population mean. b. Suppose a sample of 60 Roy-West employees showed a sample mean year-end bonus of $150,000. Assume a population standard deviation of $20,000 and compute the p-value. c. with α=0.05 as level of significance, what is your conclusion? d. Repeat the preceding hypothesis test using critical value approach.

Answer 1

Given:

= 130,500, sample size (n) = 60, sample mean () = 150,000, = 20,000

a)

Ho: = 130,500

Ha: > 130,500

b) sample size (n) = 60, sample mean () = 150,000, = 20,000

Test statistic:

P-value: 0.00001

C)

P-value < , i.e. 0.00001 < 0.05, that is Reject Ho at 5% level of significance.

d)

Critical value:

Z = Z_0.05 = 1.645

Test statistic > Critical value, i.e. 7.55 > 1.645, That is Reject Ho at 5% level of significance.

Therefore, the year end bonuses paid by Roy-West where greater than the population mean.