Question

As the Executive Vice President of Sales for ACME Nose Hair Trimmers Inc., your sales force is divided into four regions: NW, SW, NE, and SE. Your CFO and HR Director have determined that you can promote 400 of your sales force in the following year, and you allocate those promotions to your Regional VPs of Sales as follows: NW gets 80, SW gets 120, and NE and SE get 100 each. (This allocation is based on the relative sizes of the regional sales forces.)

Your employees identify themselves by hair color, and when the promotions have been completed, your HR Director presents you with a demographic break-down of regional promotions by hair color as follows:

			REGION
		NW	SW	NE	SE
HAIR	Brunette	30	30	40	25
COLOR	Brown	20	20	20	15
	Blond	10	40	20	25
	Red	10	20	10	15
	Gray	5	0	10	5
	Bald	5	10	0	15

1. You receive a number of complaints from your employees that this year’s promotions were not assigned fairly (in that some VPs favored different hair colors), so you decide to determine if the distribution of promotions differed by region. You conduct a hypothesis test to this effect.

a. State your null hypothesis for this test.

b. State your alternative hypothesis for this test.

c. Describe the Type I error for this test and what its implications are for ACME NHT Inc.

d. Describe the Type II error for this test and what its implications are for ACME NHT Inc.

e. What is the critical value of your test statistic if you are willing to reject your null hypothesis at the a = .05 level of significance? (Ensure you identify what type of statistic it is.)

f. What is the calculated value of your test statistic? (Show as much work as necessary to ensure partial credit if you are not confident of your answer.)

g. What is the p-value for this test? What does it represent?

h. What do you conclude about your hypothesis test, and why?

i. What action will you take as the Executive Vice President of Sales?

Answer 1