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MASTER’S DEGREE PROGRAMME IN BUSINESS ADMINISTRATION Module: ADVANCED QUANTITATIVE METHODS FOR MANAGERS (MBA60) Academic Year: 2017-18 1st Written Assignment (WA1) A restaurant survey was conducted by a popular guide publisher for travelers to rank the quality of fine dining restaurants in two major cities of Greece: Athens and Thessaloniki. Customers evaluated the restaurants of Athens and Thessaloniki via a questionnaire for the cost of meal per person, and issues related to the quality of food, the décor of the restaurant, the customer service, etc., all measured on a five-point scale. The dataset in the file MBA60_1718_WA1.xls gives the results of the survey from a sample of 100 restaurants (50 restaurants in Athens and 50 in Thessaloniki). The file gives the average cost of the meal per person (Variable: Meal Cost per Person) and the Overall Customer Satisfaction (Variable: Overall Customer Satisfaction). The Overall Customer Satisfaction was computed as a weighted average among the answers of all the respondents and the different aspects of customers’ satisfaction investigated. (Scale 1: very dissatisfied - 5: very satisfied) Question 1: (15%) Consider the variable: Meal Cost per person. 1.1 Construct the frequency distribution and the percentage distribution of the variable for the 50 restaurants in Athens. 1.2 Construct the frequency distribution and the percentage distribution of the variable for the 50 restaurants in Thessaloniki. 1.3 What conclusions can you reach concerning differences for the meal cost per person between the 50 restaurants in Athens and the 50 restaurants in Thessaloniki? 1.4 Plot histograms of frequency distributions of the variable (in two different graphs) for the 50 restaurants in Athens and the 50 restaurants in Thessaloniki and comment on the main characteristics of the two distributions. Question 2: (20%) 2.1 Use the original data to compute the Mean, 1st Quartile, Median, 3rd Quartile, and the Mode of the Meal Cost per person for the 50 restaurants in Athens. Interpret the summary measures you calculated. 2.2 Use the original data to compute the Mean, 1st Quartile, Median, 3rd Quartile, and the Mode of the Meal Cost per person for the 50 restaurants in Thessaloniki. Interpret the summary measures you calculated. 2.3 Compute the coefficients of skewness of the Meal Cost per person for the 50 restaurants in Athens, as well as for the 50 restaurants in Thessaloniki. What conclusions can you reach from these results? Are the data skewed? If so, how? Is this in accordance with the results of question 1.4? 1 MASTER’S DEGREE PROGRAMME IN BUSINESS ADMINISTRATION Question 3: (15%) 3.1 Use the original data to compute the Standard Deviation and Coefficient of Variation of the Meal Cost per person for 50 restaurants in Athens and 50 restaurants in Thessaloniki. 3.2 Use the original data to compute the Standard Deviation and Coefficient of Variation of the Overall Customer Satisfaction for 50 restaurants in Athens and 50 restaurants in Thessaloniki. 3.3 On the basis of the results of Question 2 through Questions 3.1 and 3.2 if you were the representative of the guide publisher for travelers, the restaurants of which city, will you suggest to your readers? Justify your answer. Question 4: (30%) 4.1 Let us assume that the variable Meal Cost per person (X) follows the normal distribution with mean 36.74 and standard deviation 9.2. Compute the Probability that a meal costs more than 50 euros (Prob (X>50)). 4.2 Given that restaurants of Thessaloniki attract 10 new customers per day on the average, calculate the probability: 4.2.1 that a given restaurant will attract more than 8 new customers, today. 4.2.2 that a given restaurant will attract more than 16 new customers, within 2 days. Question 5: (20%) An existing restaurant in Athens is closed. Thirty percent of today’s customers will visit the nearest restaurant instead. Among 15 of those customers, what is the probability: 5.1 that less than 4 will visit this particular restaurant? 5.2 that at least 2 will visit this particular restaurant? Note: You can use  the Tables of Cumulative Binomial Distribution or the Excel function : BINOMDIST(X;n;p;TRUE)  the Tables of Poisson Distribution or the Excel function : POISSON. DIST(X; mean value;TRUE)  the tables of Normal Distribution or Excel function : NORM.DIST(X; mean value; standard deviation;TRUE) 2 MASTER’S DEGREE PROGRAMME IN BUSINESS ADMINISTRATION Assignment guidelines          It is important that the coursework reflects your knowledge rather than it being simply an accumulation of information. The assignment should be well structured and easy to read. The assignment should clearly present all aspects and perspectives of the subject area, i.e.: o efficiently develop all necessary elements o refer to actual case studies or statistics if required o present reasonable argumentation o omit irrelevant material All questions are compulsory. The assignment, including possible diagrams, tables, references etc., should not exceed 5000words. For every additional 1000 words there will be a penalty of 0.5 points. Each question accounts for a percentage of the total mark. This is clearly marked at the beginning of each question. The assignment is due on 05/12/2017. Please note that no assignment will be acceptable after this date as the electronic submission system automatically locks at 23:59 on the last day of submission. You should submit your assignment via http://study.eap.gr (or http://study.hou-wue.eu if you attend the HOU-WUE MBA Programme) using your username and password. You may use any of the following file formats: o Microsoft Word or / and Excel 97-2003 (*.doc / *.xls). o Microsoft Word or / and Excel Open XML (*.docx / *.xlsx) o Note: Interpretation of results and other text must be submitted ONLY in Word format. Other document formats or read only file formats such as Portable Document Format (*.pdf) are not acceptable formats for the submission of your assignment. Please pay attention to the proper naming of your assignment. The file should be named as follows: Surname-Initial-WAnumber-YourClass. For example, if your name is Peter Drucker, you are sending in your 3rd assignment, and you are in ATH1 Class, then you should name your file as follows: Drucker-P-WA3-ATH1. Assignments that fail to comply with this requirement will receive a lower mark in the presentation grade. Copying is considered cheating and is not acceptable in any form. Copying large parts or whole paragraphs of text found in any of the sources used for an assignment (printed books, academic articles, or electronic media of any kind) is totally unacceptable. It is considered plagiarism and leads to a severe penalty for the student(s) involved. Students should cite all sources from which they take data, ideas or words, whether quoted directly or paraphrased. Good luck!! 3 Location Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Meal cost per person (in euros) 50 38 43 56 51 36 25 33 41 44 34 39 49 37 40 50 50 35 22 45 44 38 14 44 51 27 44 39 50 35 31 34 48 48 30 42 26 35 32 Overal Customer Satisfaction 3.17 3.00 3.17 3.83 3.83 3.83 3.33 3.33 3.17 3.50 3.33 3.50 4.00 3.33 2.83 3.50 3.50 3.33 2.83 3.50 3.83 2.83 3.67 3.17 3.50 3.17 3.17 3.50 4.00 3.17 2.83 3.17 3.67 3.67 2.33 3.67 3.33 3.00 3.00 Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Athens Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki 63 36 38 53 23 39 45 37 31 39 53 37 37 29 38 37 38 39 29 36 38 44 27 24 34 44 23 30 32 25 29 43 31 26 34 23 41 32 30 28 33 26 4.00 3.50 3.00 3.33 3.50 3.17 3.00 3.33 3.50 3.17 3.50 3.00 2.33 2.83 3.17 3.67 3.00 3.17 3.00 3.00 3.33 3.33 3.00 2.33 2.83 3.83 2.83 2.33 3.17 2.50 2.00 3.17 3.50 2.17 2.83 2.83 3.33 2.67 2.83 1.83 2.67 2.00 Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki Thessaloniki 51 26 48 39 55 24 38 31 30 51 30 27 38 26 28 33 38 32 25 4.17 2.83 3.67 3.00 3.33 1.83 3.00 3.50 3.17 4.50 3.00 2.67 3.33 2.67 2.00 4.00 3.00 2.50 2.33
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Running Head: BUSINESS STATISTICS

1

Advanced quantitative methods for managers (mba60)

Your Name
Institution Affiliations

BUSINESS STATISTICS

2

Business statistics
Module: ADVANCED QUANTITATIVE METHODS FOR MANAGERS (MBA60)
A famous guide publisher conducted a survey in two major cities of Greece, Thesaloniki and
Athens about restaurants. Customers were given questionnaires to fill and give back their
feedback. They analyzed the cost of meals served in hotels in these two cities and their quality,
customer services offered and many other. The results
Results and Analysis
50 restaurants in Athens and 50 in Thessaloniki were examined and the results were attached in
the excel file for analysis as shown in the below and in the excel file attached.
Question 1: Solution
1.1
Following table shows the frequency distribution and percentage distribution for 'Athens":
Classes

Frequency , f

Percentage (%),[ (f/50)*100]

11-15

1

2

15-20

0

0

20-25

2

4

25-30

3

6

30-35

7

14

35-40

14

28

40-45

8

16

45-50

5

10

50-55

8

16

55-60

1

2

60-65

1

2

Total

50

100

1.2
Following table shows the frequency distribution and percentage distribution for "Thessaloniki":
Classes Frequency , f

Percentage (%),[ (f/50)*100]

11-15

0

0

15-20

0

0

BUSINESS STATISTICS

3

20-25

4

8

25-30

13

26

30-35

13

26

35-40

12

24

40-45

4

8

45-50

1

2

50-55

2

4

55-60

1

2

60-65

0

0

Total

50

100

1.3:
It seems that meal cost per person is greater in Athens. Approximate 50% of meal cost in Athens
are less than 40 while around 84% of meal cost in Thessaloniki is less than 40.
1.4:
Following are the histograms:

BUSINESS STATISTICS

4

Distribution of meal cost per person in Athens is approximately symmetric while meal cost per
person in Thessaloniki is skewed to right.

Question 2: Solution
2.1.
Mean = ∑x / n = 1987/50 = 39.74
To find quartiles, first arrange the data in ascending order
Athens
order
value
1
14
2
22
3
23
4
25
5
26
6
27
7
30
8
31
9
31
10
32
11
33
12
34
13
34

BUSINESS STATISTICS
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50

5

35
35
35
36
36
37
37
38
38
38
39
39
39
39
40
41
42
43
44
44
44
44
45
45
48
48
49
50
50
50
50
51
51
53
53
56
63

1st Quartile Q1 = [(n+1)/4]th term = [(50+1)/4]th term = 12.75th term = 12th term + 0.75*[13th
term - 12th term]
= 34 + 0.75*[34 - 34] = 34


1st Quartile = 34

Median= [(n+1)/2]th term = [(50+1)/2]th term = 25.5th term = 25th term + 0.5*[26th term - 25th
term]

BUSINESS S...


Anonymous
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