QUANTITATIVE METHODS – JUNE 2021
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QUANTITATIVE METHODS – JUNE 2021
Case Study 1 Maximum Word Limit 1000 words
Maple Leaf Hotels operate hotels throughout Canada. The head of Customer Relations conducted a survey of customer satisfaction in two hotels; one in Winnipeg and one in Quebec. The hotel in Winnipeg had an average score of 57 and a standard deviation of 7, while the hotel in Quebec had an average score of 58 and a standard deviation of 6. In each hotel there were 51 customers surveyed.
(i) Use an appropriate hypothesis test to show whether the average score for the Quebec hotel is significantly higher than the score for the Winnipeg hotel. (5 marks)
(ii) Use an appropriate hypothesis test to determine whether the variance in the
Winnipeg hotel is significantly higher than the variance in the Quebec hotel. (5 marks)
(iii) Write a report on your findings, detailing any assumptions you have made and any
further information that should be obtained. (15 marks) (Total 25 marks)
Case Study 2 Maximum Word Limit 1000 words
i) Personal daily water usage in New Zealand has been found to be normally distributed with a mean of 24 gallons and a variance of 39 gallons2 .
(a) What percentage of the population uses more than 33 gallons?
(b) What percentage of the population uses between 16 and 27 gallons?
(c) What percentage of the population uses more than 20 gallons?
(d) What percentage of the population uses less than 26 gallons?
(e) What is the probability of finding a person who uses less than 12 gallons? (5 marks)
(ii) As there is always a water shortage in New Zealand, the Prime Minister has decided
to give a tax rebate to the 22% of the population who use the least amount of water.
What should the Prime Minister set as the maximum water usage for a person to qualify for a tax rebate? (3 marks)
(iii) The possibility of obtaining a tax rebate has caused a decrease in the mean daily
water usage to 20 gallons per person. The variance is unchanged.
What should the level of maximum water usage now be set at to ensure that the same proportion of the population would qualify for a tax rebate? (3 marks)
iv) Describe the characteristics of the Normal Distribution. Explain the importance of this distribution in management decision-making, giving at least three examples. (14 marks) (Total 25 marks)
Case Study 3 Maximum Word Limit 1000 words
A consultant for a marketing agency is looking at how much time different age groups in society spend reading on a daily basis. The agency is interested in finding out whether there is a relationship between a person’s age and the amount of time they spend reading. The data for a random sample of 20 respondents are shown in the table below.
Respondent Age (years) Number of Hours
Reading per Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
x
44
52
56
57
59
57
72
35
62
41
54
62
60
51
38
55
47
65
50
61
y
8
1
3
0
5
7
10
1
8
2
6
10
9
6
1
5
2
7
4
5
The following statistics have been calculated:
∑ (x − x )2 = 1669.8
∑ (y − y )2 = 190
∑ (y − y )(x − x) = 366
(i) Find the equation of the least squares regression line. (3 marks)
(ii) Calculate the correlation coefficient and interpret the result. (3 marks)
(iii) Calculate the R-squared value and interpret the result. (2 marks)
(iv) How many hours reading in a day would you expect in:
(a) An individual aged 60?
(b) An individual aged 34?
Which of the above estimates of the number of hours reading would you expect to be more accurate, and why? (2 marks)
(v) Write a report from the consultant to the owner of the marketing agency on the analysis of the data. Indicate any additional information you would require and include any recommendations for further analysis. (15 marks) (Total 25 marks)
Case Study 4 Maximum Word Limit 1000 words
The production manager of a firm that produces mobile phone cables wishes to forecast the monthly demand for its products. The table below shows recent demand for the cables.
|
Monthly Demand for Phone Cables |
|
|
March to September 2020 |
|
|
Month |
Demand |
|
|
(thousands) |
|
March |
191 |
|
April |
157 |
|
May |
234 |
|
June |
300 |
|
July |
276 |
|
August |
223 |
|
September |
311 |
(i) Use a three-point moving average to compute a forecast of demand for cables in October. (4 marks)
(ii) Use exponential smoothing with α = 0.2 to compute a forecast for October. (4 marks)
(iii) Use exponential smoothing with α = 0.6 to compute a forecast for October. (4 marks)
(iv) Write a report on your findings for the manager. Indicate the most appropriate
forecasting method for these data, giving advantages and disadvantages of each. (13 marks) (Total 25 marks)
TOTAL OF 100 MARKS
2023-07-10