Group Assignment -
Question 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?
Question 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.
Question 3 - The following are the results from a completely randomized design consisting of 3 treatments.
|
Source of Variation
|
Sum of Squares
|
Degree 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.
Question 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?
Note - MS Excel must be used for performing calculation/graphical presentation as required in this assignment.