QUANTITATIVE METHODS – AUGUST 2020
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QUANTITATIVE METHODS – AUGUST 2020
Case Study 1 Maximum Word Count 1000 words
Le Gourmet produces speciality French cakes such as eclairs and croissants. The company introduced an incentive scheme that rewards employees for increased levels of productivity one year ago. The Managing Director is interested in finding out if the incentive scheme has had a significant effect on productivity levels in the factory. Below is the output for a sample of employees on a shift before the incentive scheme was started and the output from those same employees on a shift in the last week.
Employee |
One year ago |
Last week |
1 |
66 |
73 |
2 |
57 |
68 |
3 |
74 |
81 |
4 |
74 |
95 |
5 |
52 |
82 |
6 |
63 |
94 |
7 |
47 |
65 |
8 |
55 |
81 |
9 |
51 |
47 |
10 |
47 |
63 |
11 |
53 |
54 |
12 |
55 |
56 |
13 |
67 |
55 |
14 |
58 |
86 |
15 |
56 |
55 |
(i) Using an appropriate hypothesis test, determine whether the average productivity in the most recent week is significantly different from the average productivity one year ago. (8 marks)
(ii) The Managing Director has now decided that she should have determined if the
productivity level was significantly higher on the shift last week than the shift one year ago. Use a suitable hypothesis test to reach a conclusion. (4 marks)
(iii) Write a report on your findings. Discuss any reservations that you may have about
the data and the hypothesis tests that have been used. (13 marks) (Total 25 marks)
Case Study 2 Maximum Word Count 1000 words
The French Post company offers a next-day delivery service for a premium price. Express parcels have to be delivered within 18 hours of being posted.
The Quality Director has been looking at delivery times of parcels in Paris. He has taken a sample of 24 parcels over a month and has collected the following data:
Express Service Delivery Times for Paris Depot (hours)
20 |
19 |
17 |
21 |
26 |
24 |
24 |
24 |
23 |
29 |
18 |
18 |
18 |
28 |
19 |
17 |
17 |
21 |
17 |
26 |
26 |
18 |
25 |
21 |
Σx = 516 Σx2 = 11,432
(i) Use an appropriate hypothesis test to determine whether the average time taken to deliver the parcels is significantly greater than the time indicated for the express service. (8 marks)
(ii) Demonstrate how the data can be used to calculate a revised quality standard using:
(a) the 95% confidence limits
(b) the 99% confidence limits (4 marks)
(iii) Write a report on your findings. Indicate any reservations you may have and the
assumptions you have made. (13 marks) (Total 25 marks)
Case Study 3 Maximum Word Count 1000 words
The owner of Café Bleu, a restaurant chain based in France, has been looking into the level of job satisfaction of various employees in her company. She categorised the jobs into levels of seniority 1 to 14, with 14 being the most senior and 1 being the least senior. (Senior management posts rated at levels 15 to 20 were not included in the survey.) Job satisfaction was rated as a score out of 80 calculated from a number of different survey questions. Choosing one person at random from each of the fourteen levels, she collected the following data.
Seniority x |
Job Satisfaction Rating y |
1 |
42 |
2 |
65 |
3 |
63 |
4 |
71 |
5 |
61 |
6 |
58 |
7 |
50 |
8 |
52 |
9 |
44 |
10 |
48 |
11 |
40 |
12 |
39 |
13 |
36 |
14 |
62 |
She also calculated the following summary statistics:
Σx = 105 Σy = 731 Σ(x- x)2 = 227.5
Σ(x- x)(y- y ) = -298.5 Σx2 = 1015 Σy2 = 39789
(i) Find the equation of the least squares regression line.
Σ(y- y )2 = 1620.36 (3 marks)
(ii) Calculate the correlation coefficient and interpret the result. (3 marks)
(iii) Calculate the R2 value and interpret the result. (2 marks)
(iv) What job satisfaction score would you expect to see for:
(b) A person working at level 18
Which of the above estimates would you expect to be more accurate, and why? (3 marks)
(v) Write a report on the analysis of the data. Indicate any additional information you would require and include any recommendations for further analysis. (14 marks) (Total 25 marks)
Case Study 4 Maximum Word Count 1000 words
AutoClair is a company specialising in cleaning car interiors. The Sales Director is looking at sales of a new product – Le Vacuum – that makes it an easier task for customers to clean their cars at home. He has been collecting data over the past nine weeks on the number of purchases of Le Vacuum. The number sold each week is summarised in the table below.
Week |
Sales |
1 |
75 |
2 |
76 |
3 |
72 |
4 |
64 |
5 |
60 |
6 |
53 |
7 |
48 |
8 |
41 |
9 |
37 |
(i) Use the method of exponential smoothing to smooth the series using a smoothing constant of 0.3. Produce a forecast of the number of purchases for each of the next two weeks. Describe any assumptions that you have made and discuss the relevance of the technique you have used, and any reservations you may have. (10 marks)
(ii) Describe the three major categories of forecasting techniques. Give at least two
relevant examples for each of the categories. (15 marks) (Total 25 marks) TOTAL OF 100 MARKS
2023-07-10