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**HOLMES INSTITUTE FACULTY OF HIGHER EDUCATION **

**Due End of Week 10**

**WORTH 30%**

**(Maximum 5 students in the group)**

**MS Excel must be used for performing calculation/graphical presentation as required in this assignment**

**Question 1 8 marks**

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

- Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set using a class width of $50.
**(3 marks)** - Construct a histogram showing the percent frequency distribution of the furniture- order values in the sample. Comment on the shape of the distribution.
**(3 marks)** - Given the shape of the distribution in part b, what measure of location would be most appropriate for this data set?
**(2 marks)**

**Question 2 6 marks**

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

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

**(2 marks)**

- Compute the coefficient of determination and fully interpret its meaning.

Be very specific. **(2 marks)**

- Compute the coefficient of correlation and explain the relationship between demand and unit price.
**(2 marks)**

**Question 3 6 marks**

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

*Sum of*

*Degrees of*

*Mean*

__Source of Variation Squares Freedom 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.

**Question 4 10 marks**

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

__Coefficient____s Standard Error__

Intercept 0.8051

x1 0.4977 0.4617 x2 0.4733 0.0387

- Develop an estimated regression equation relating y to x1 and x2.
**(2 marks)** - 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.**(2 marks) **

c. At α = 0.05, test to see if β1 and β2 is significantly different from zero. **(2 marks) **

d. Interpret slope coefficient for X2 **(2 marks) **

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? **(2 marks)**

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