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1. Missy Walters owns a mail-order business specializing in clothing, linens, and furniture for children. She is considering offering her customers a discount on shipping charges for furniture based on the dollar-amount of the furniture order. Before Missy decides the discount policy, she needs a better understanding of the dollar-amount distribution of the furniture orders she receives.

Missy had an assistant randomly select 50 recent orders that included furniture. The assistant recorded the value, to the nearest dollar, of the furniture portion of each order. The data collected is listed below (data set also provided in accompanying MS Excel file).

136

281

226

123

178

445

231

389

196

175

211

162

212

241

182

290

434

167

246

338

194

242

368

258

323

196

183

209

198

212

277

348

173

409

264

237

490

222

472

248

231

154

166

214

311

141

159

362

189

260

 
a. Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set using a class width of $50.  
 
b. Construct a histogram showing the percent frequency distribution of the furniture- order values in the sample. Comment on the shape of the distribution.
 
c. Given the shape of the distribution in part b, what measure of location would be most appropriate for this data set?                                                                     
2. Shown below is a portion of a computer output for a regression analysis relating Y (demand) and X (unit price).
 

ANOVA

 

 

 

df

SS

Regression

1

5048.818

Residual

46

3132.661

Total

47

8181.479

 

Coefficients

Standard Error

Intercept

80.390

3.102

X

-2.137

0.248

a. Determine whether or not demand and unit price are related. Use α = 0.05.

b. Compute the coefficient of determination and fully interpret its meaning. Be very specific.                                                                                        

c. Compute the coefficient of correlation and explain the relationship between demand and unit price.                                                              

3. The following are the results from a completely randomized design consisting of 3 treatments.

 

Source of Variation

Sum of

Squares

Degrees of

Freedom

Mean

Square

 

F

Between Treatments

390.58

 

 

 

Within Treatments (Error)

158.40

 

 

 

Total

548.98

23

 

 

Using α = .05, test to see if there is a significant difference among the means of the three populations. The sample sizes for the three treatments are equal.

4. In order to determine whether or not the number of mobile phones sold per day (y) is related to price (x1 in $1,000), and the number of advertising spots (x2), data were gathered for 7 days. Part of the Excel output is shown below.

ANOVA

 

df

 

SS                        MS              F

Regression

 

40.700

Residual

 

1.016

 

Coefficients

Standard Error

Intercept

0.8051

 

x1

0.4977

0.4617

x2

0.4733

0.0387

a. Develop an estimated regression equation relating y to x1 and x2.                 

b. At α = 0.05, test to determine if the estimated equation developed in Part a represents a significant relationship between all the independent variables and the dependent variable.

c. At α = 0.05, test to see if β1 and β2 is significantly different from zero.           

d. Interpret slope coefficient for X2.                                                                       

e. If the company charges $20,000 for each phone and uses 10 advertising spots, how many mobile phones would you expect them to sell in a day?      

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