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HOLMES INSTITUTE FACULTY OF HIGHER EDUCATION HI6007 Group Assignment

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 ran domly 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.
- Construct a histogram showing the percent frequency distribution of the furniture - order values in the sample. Comment on the shape o f the distribution.
- Given the shape of the distribution in part b, what measure of location would be most appropriate for this data set?

Shown below is a portion of a computer output for a regression analysis relating Y (demand) and X (unit price).

- Determine whether or not demand and unit price are related. Use α = 0.05.
- Compute the coefficient of determination and fully interpret its meaning. Be very specific.
- Compute the coefficient of correlation and explain the relationship between demand and un it price.

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

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.

In order to determine whether or not the number of mobile phones sold per day (y) is related to price (x 1 in $1,000), and the number of advertising spots (x 2 ), data were gathered for 7 days. Part of the Excel output is shown below.

- Develop an estimated regression equation relating y to x1 and x2
- 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.
- At α = 0.05, test to see if β1 and β2 is significantly different from zero.
- Interpret slope coefficient for X2.
- 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?

MS Excel must be used to perform any calculations/graphical presentations as required in this assignment

Question 1

Below you are given the examination scores of 20 students (data set also provided in accompanying MS Excel file).

52 99 92 86 84

63 72 76 95 88

92 58 65 79 80

90 75 74 56 99

- Construct a frequency distribution, cumulative frequency distribution, relative frequency distribution, cumulative relative frequency distribution and percent frequency distribution for the data set using a class width of 10.
- Construct a histogram showing the percent frequency distribution of the examination scores. Comment on the shape of the distribution.

Question 2

Shown below is a portion of a computer output for a Regression analysis relating supply (Y in thousands of units) and unit price (X in thousands of dollars).

ANOVA df SS Regression 1 354.689 Residual 39 7035.262 Coefficients Standard Error Intercept 54.076 2.358 X 0.029 0.021

- What has been the sample size for this problem?
- Determine whether or not supply and unit price are related. Use α = 0.05.
- Compute the coefficient of determination and fully interpret its meaning. Be very specific.
- Compute the coefficient of correlation and explain the relationship between supply and unit price.
- Predict the supply (in units) when the unit price is $50,000.

Question 3

Allied Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below (data set also provided in accompanying MS Excel file).

Program A Program B Program C Program D 150 150 185 175 130 120 220 150 120 135 190 120 180 160 180 130 145 110 175 175

- Construct an ANOVA table.
- As the statistical consultant to Allied, what would you advise them? Use a .05 level of significance.

Question 4

A company has recorded data on the weekly sales for its product (y), the unit price of the competitor's product (x1), and advertising expenditures (x2). The data resulting from a random sample of 7 weeks follows. Use Excel's Regression Tool to answer the following questions (data set also provided in accompanying MS Excel file).

Week Price Advertising Sales 1 .33 5 20 2 .25 2 14 3 .44 7 22 4 .40 9 21 5 .35 4 16 6 .39 8 19 7 .29 9 15

- What is the estimated regression equation? Show the regression output.
- Determine whether the model is significant overall. Use α = 0.10.
- Determine if competitor’s price and advertising is individually significantly related to sales. Use α = 0.10.
- Based on your answer to part (c), drop any insignificant independent variable(s) and re-estimate the model. What is the new estimated regression equation?
- Interpret the slope coefficient(s) of the model from part (d).

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