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 thea = .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?

2. Because of further employee complaints, the ACLU becomes involved in a discrimination lawsuit against ACME NHT Inc., accusing you of discriminatory promotion practices within your sales force. You immediately ask your HR Director for the distribution of your total sales force by hair color (expressed as percentages). She provides you with the following data:

Brunette	Brown	Blond	Red	Gray	Bald
30%	20%	25%	12%	5%	8%

You decide to conduct a hypothesis test to determine if your total promotions follow the distribution of the demographics of your sales force.

a. State your null hypothesis.

b. State your alternative hypothesis.

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. Fill in the following table with your expected number of promotions for each hair color if H₀ is true. (Recall you had a total of 400 promotions.)

Brunette	Brown	Blond	Red	Gray	Bald

f. What is the critical value of your test statistic if you are willing to reject your null hypothesis at thea = .10 level of significance? (Ensure you identify what type of statistic it is.)

g. 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.)

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

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

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

3. The ACME NHT Inc. Executive Vice President of Marketing is considering a national advertising campaign, and asks you if the averages of your quarterly sales differ significantly by region. You already have available your quarterly sales totals for each region (in millions of dollars). They are as follows:

		REGION
	NW	SW	NE	SE
Q1	5	7	8	4
Q2	7	6	7	6
Q3	3	5	9	5
Q4	6	4	6	3

You decide to test if there is a statistical difference in your quarterly regional sales averages.

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 thea = .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?

j. Which two regions are most likely different from each other in sales performance?

4. In your attempt to "catch them all" you hunt the prized Pokemon, Mew and Mewtwo. As you battle them with your top 25 Pokemon, you lose every battle. However, after each battle, you notice that the hit points (HP) of Mew and Mewtwo have been reduced. The remaining HPs of Mew and Mewtwo are shown below after battling your respective Pokemon. (A higher HP remaining indicates more success in battle.) You suspect that Mewtwo is the tougher opponent, and you want to test this hypothesis at the 95% level of confidence.

Attacker	Mew	Mewtwo
Bulbasaur	402	377
Ivysaur	305	354
Venusaur	348	343
Charmander	350	341
Charmeleon	320	347
Charizard	340	401
Squirtle	396	406
Wartortle	311	364
Blastoise	367	381
Caterpie	309	402
Metapod	391	387
Butterfree	385	347
Weedle	390	349
Kakuna	313	402
Beedrill	396	403
Pidgey	394	389
Pidgeotto	329	395
Pidgeot	375	356
Rattata	364	340
Raticate	340	400
Spearow	365	405
Fearow	395	402
Ekans	365	377
Arbok	396	341
Pikachu	381	399

Assume that before each battle, Mew and Mewtwo started with the same number of HPs.

a. State the null hypotheses for this test.

b. State the alternative hypotheses for this test.

c. What type of test will you use to test this hypothesis?

d. Describe the Type I Error for this test, and explain its implication for you as you continue your quest.

e. Describe the Type II Error for this test, and explain its implication for you as you continue your quest.

f. What is the rejection region for this hypothesis test?

g. Calculate the test statistic for this hypothesis test. What is your conclusion?

h. If you reject the null hypothesis for this test, what is the probability that you have committed a Type I Error? (i.e., find the p-value for this test.)

i. What action will you take as you continue your quest based on your conclusion.

j. Which do like better: Mew or Mewtwo?

5. You conduct an experiment where you collect the data in the table below. What population distribution does this sample come from? How confident are you of your conclusion?

14.79911	28.23858	22.7928	24.51667	22.50702
35.50089	21.75057	28.08752	23.47746	17.71201
26.95663	28.87379	30.59481	30.82701	24.77064
23.74223	25.52936	29.04185	36.87479	30.37362
27.93906	21.90754	26.42687	19.92638	22.93284
24.13246	20.7254	24.26107	18.39259	27.64909
34.6292	18.9683	13.42521	26.82254	31.90741
24.89723	27.22881	19.47299	29.76344	32.58799
16.85994	29.5746	27.5072	25.65619	15.6708
27.36716	27.79298	26.68962	22.06142	23.07119
31.60902	26.03893	32.98606	28.54943	20.34101
33.44006	26.55777	21.08564	23.87313	23.20798
29.21436	25.27635	28.70976	29.39177	22.21248
19.70519	23.34337	25.02365	16.32654	25.40277
22.36094	32.23156	22.65091	20.90823	33.97346
18.69098	19.22807	23.61038	30.16207	21.59024
28.39246	31.3317	26.16754	27.09202	20.13793
25.91088	20.53656	17.31394	21.42621	31.07193
24.64381	18.06844	26.29683	29.72477	24.00317
25.15	29.95899	21.25815	24.38912	25.78333

6. Going back to the home sales data for Delta County, CO (see your Project 1 work) you want to see when the market peaked and where it seemed to return to its previous levels. You consider the average sale price for the County for different years.

a. Can you determine if the market peaked in 2007 or 2008? (Is there a difference between the averages prices in these two years?)

b. Can we conclude that in 2010 and 2011 that the market had returned to 2006 levels?

c. Did the market increase from 1995 to 2007? Are you sure?

7. For this problem, use the data file STAT4610Projecdt3ResidentialData2009. This file contains data on 75% of the homes sold in Colorado in 2009 (Sales2009 tab) and data on the listing real estate agents for those homes (Listing Broker Data tab). We are interested in investigating the differences in the "Big 5" Realtor Associations in Colorado (identified under the "Board" field):

Aurora Association of Realtors

Boulder County

Denver Metro Association of Realtors (Not Denver Metro Comm)

Douglas/Elbert Realtor Association

South Metro Denver Realtor Association

The data we are interested in is "Close Price," i.e., the actual price the homes sold for.

Unfortunately, the Sales tab does not have the Realtor Association included, so the two files must be merged through a common key. (Fortunately, there is one!) The List Agent MLSID is a unique identifier for the listing agents, and it is included with the Sales data.

By filtering out the close price data by Association and answer the following questions.

a. What are the average closing prices for each Association in 2009.

b. Are any of the averages different from the rest? (Justify your answer with an appropriate test and a p-value.)

c. Is there a difference between Boulder and South Metro? (Justify your answer with an appropriate test and a p-value.)

d. Is there a difference between Aurora and Douglas/Elbert? (Justify your answer with an appropriate test and a p-value.)

e. Is there a difference between South Metro and Denver Metro? (Justify your answer with an appropriate test and a p-value.)

f. Is there a difference between Boulder and Douglas/Elbert? (Justify your answer with an appropriate test and a p-value.)