### Statistical Methods II

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UU-MTH-3000 Statistical Methods II
Assignment 2: 20 per cent of module grade
Assignment 2 – Brief & Guidelines
This is an individual assignment.
Solve all of the following questions.
Reproduction of someone else’s work as your own will be penalized.
This Assignment is due at the end of Week 3; Sunday 11:59pm (23:59 hours) VLE (UTC)
time on the due date at the latest.
Late submission is not accepted.
The maximum grade of this assignment is 100.
This assignment carries a 20% weight of the final grade for this module.
Submit one single document and not lots of different files.
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Assignment 2 Part A – ANOVA
1. A manager at the head office of a company is considering 3 branch office managers for
promotion. Branch reports include records of sales volume per agent for each branch. A
random sample of records was selected for agents at each branch. All branches are
located in cities with similar demographics (per capita income, population etc.) Using the
samples, the manager wants to see if there is a significant difference in performance of
agents at the three branches. If there is a difference, the information will be used to help
determine which branch manager to promote; otherwise it will not be included in the
decision. (All values are in hundreds of thousands of dollars.)
(15 points)

 Branch Managed Branch Managed Branch Managed by Harrison by Dale by Stevenson 7.2 8.8 6.9 6.4 10.7 8.7 10.1 11.1 10.5 11 9.8 11.4 9.9 10.6

For the single measurement problem, use an a = 0.01 level of significance. Conduct an
appropriate hypothesis test and conclude whether to reject or not reject the claim that
there is no difference among the agents at the different branches.

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Assignment 2 Part B – Regression
1. Each box of one brand of breakfast cereal contains a coupon entitling purchasers to a
free package of vegetable seeds. At the home office, they use the weight of the incoming
mail to determine the number of employees to be assigned to collecting coupons and
sending out seed packages each day. (The company policy is that all mail received will be
answered the same day.) Following is the data for a random sample of 8 days:
(15 points)

 Weight of mail (pounds) 11 20 16 6 12 18 23 25 Number of employees 6 10 9 5 8 14 13 16

a. Draw a scatter diagram for the data and discuss its shape.
b. Using Excel conduct the following regression modules for the data:

 I. Linear II. III. IV. Quadratic Third degree polynomial Exponential

V. Logarithmic
VI. Power
c. Determine which model is the best and state the reason for your choice.
d. What percentage of the variation in the number of employees is explained by the
regression model chosen?
e. If the company receives 15 pounds of mail, how many employees should be assigned for
mail duty?

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Assignment 2 Part C – Time Series and Non-Parametric Tests
1. The number of fishing rods selling each day is given below. Perform analyses of the time
series to determine which model should be used for forecasting.
(10 points)
a. 3 day moving average analysis
b.
4 day moving average analysis
c.
3 day weighted moving average analysis with weights w1=0.2, w2=0.3 and w3=0.5 with
w1 on the oldest data
d.
exponential smoothing analysis with a = 0.3.
e. Which model provides a better fit of the data?
f. Forecast day 13 sales of fishing rods using the model chosen in part (e).

 Day Rods sold 1 60 2 70 3 110 4 80 5 70 6 85 7 115 8 105 9 65 10 75 11 95 12 85