3000 Statistical Methods II

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Page 1 of 4UU-MTH-3000 Statistical Methods IIAssignment 2: 20 per cent of module gradeAssignment 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.Page 2 of 4Assignment 2 Part A – ANOVA1. A manager at the head office of a company is considering 3 branch office managers forpromotion. Branch reports include records of sales volume per agent for each branch. Arandom sample of records was selected for agents at each branch. All branches arelocated in cities with similar demographics (per capita income, population etc.) Using thesamples, the manager wants to see if there is a significant difference in performance ofagents at the three branches. If there is a difference, the information will be used to helpdetermine which branch manager to promote; otherwise it will not be included in thedecision. (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 anappropriate hypothesis test and conclude whether to reject or not reject the claim thatthere is no difference among the agents at the different branches.Page 3 of 4Assignment 2 Part B – Regression1. Each box of one brand of breakfast cereal contains a coupon entitling purchasers to afree package of vegetable seeds. At the home office, they use the weight of the incomingmail to determine the number of employees to be assigned to collecting coupons andsending out seed packages each day. (The company policy is that all mail received will beanswered 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.
QuadraticThird degree polynomialExponential
V. LogarithmicVI. Powerc. 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 theregression model chosen?e. If the company receives 15 pounds of mail, how many employees should be assigned formail duty?Page 4 of 4Assignment 2 Part C – Time Series and Non-Parametric Tests1. The number of fishing rods selling each day is given below. Perform analyses of the timeseries to determine which model should be used for forecasting. (10 points)a. 3 day moving average analysisb. 4 day moving average analysisc. 3 day weighted moving average analysis with weights w1=0.2, w2=0.3 and w3=0.5 withw1 on the oldest datad. 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
2. Please read the relevant article, found in the VLE, before answering this question.Discuss the process and findings used in the study of the article. Suggest a possiblestudy that could be done at your current or past job that could use a similarmethodology and analysis. (10 points)

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