+1 862 207 3288 Produce one cross tabulation (what is cross tabulation) in order to investigate any possible association between two appropriate categorical variables.
Comment on the results and make relevant recommendation to Hotel’s management
P.S. Attached example of cross tabulation for your ref.
Descriptive Statistics – categorical variables: Region
According to the data which given on the pages ??, which data was provided by 104 hotels. After collected the 104 surveys from the hotels, found two outline data on -1 data on distance from the nearest from the rail link and -1 data on the service years of the hotel managers. So, we decided ignore these two surveys data. However, the total of the surveys from the hotels are 102 only.
Region
Mean 1.892156863
Standard Error 0.081133092
Median 2
Mode 1
Standard Deviation 0.819404067
Sample Variance 0.671423025
Kurtosis -1.482360029
Skewness 0.203161078
Range 2
Minimum 1
Maximum 3
Sum 193
Count 102
Country No. of Hotel
1- Finland 40
2 – Sweden 33
3 – Norway 29
Total 102
The total of the hotel is 102, 40 of the hotels are located in Finland, it is 39% of the total.
The second one 33 hotels are located in Sweden, 32 % of the total. Norway is 29% of the total, only 29 hotels in there.
Descriptive Statistics – categorical variables: Size of the Hotel
Size of Hotel
Mean 1.81372549
Standard Error 0.080921686
Median 2
Mode 1
Standard Deviation 0.817268963
Sample Variance 0.667928558
Kurtosis -1.413014183
Skewness 0.358131814
Range 2
Minimum 1
Maximum 3
Sum 185
Count 102
No. of rooms No. of Hotel
1 = < 50 45
2 = 50-100 31
3 = >100 26
Total 102
This figure shows that 45 Hotels of the total 102 is less that 50 rooms, 44% of the total.
Only 26% of the Hotels are operating more than 100 rooms.
Descriptive Statistics – categorical variables: Gender of the manager
Gender of the manager
Mean 1.411764706
Standard Error 0.04897105
Median 1
Mode 1
Standard Deviation 0.494583357
Sample Variance 0.244612697
Kurtosis -1.905300144
Skewness 0.363942696
Range 1
Minimum 1
Maximum 2
Sum 144
Count 102
Gender of manager No. of person
1- Male 60
2- Female 42
Total 102
In 102 hotel managers, 60 managers are male to take 59% of the total. The rest of 41% managers are female.
Descriptive Statistics – Categorical variables: Years of service
Years of service
Mean 1.519607843
Standard Error 0.061890228
Median 1
Mode 1
Standard Deviation 0.625060665
Sample Variance 0.390700835
Kurtosis -0.353077889
Skewness 0.793077803
Range 2
Minimum 1
Maximum 3
Sum 155
Count 102
Service years No. of manager
1 = 0-3 years 56
2 = 4-7 years 39
3 = > 7 years 7
Total 102
The survey of the service year is 55% of the managers are working in the hotel between 0-3 years. Less than 7% of the managers are working over 7 years.
Descriptive Statistics – numerical variables: Distance
Firstly, the categorical variables which are: Distance, Advertising, Employees, Type A and B.
Distance (miles)
Mean 2.431372549
Standard Error 0.091962262
Median 2.5
Mode 1.5
Standard Deviation 0.92877332
Sample Variance 0.86261988
Kurtosis -1.097970621
Skewness 0.062529806
Range 3.5
Minimum 0.5
Maximum 4
Sum 248
Count 102
Distance (miles) frequency
0.5-1 1
1-1.5 15
1.5-2 16
2-2.5 18
2.5-3 15
3-3.5 17
3.5-4 20
Grand Total 102
According to the Distance (in miles) chart, the nearest distance between hotel and rail link is 0.5 miles, the longest distance is 4 miles, the mode is 1.5 miles.
The mean is 2.43 and the median is 2.5, figures are closed together.
Descriptive Statistics – numerical variables: Advertising
Advertising (£)
Mean 1223.04902
Standard Error 28.70686225
Median 1198.5
Mode 1460
Standard Deviation 289.9250971
Sample Variance 84056.56193
Kurtosis -1.113213947
Skewness 0.020149338
Range 1147
Minimum 651
Maximum 1798
Sum 124751
Count 102
Advertising frequency
600-699 1
700-799 2
800-899 20
900-999 3
1000-1099 11
1100-1199 14
1200-1299 7
1300-1399 10
1400-1499 15
1500-1599 11
1600-1699 2
1700-1800 6
Grand Total 102
The Advertising (£) table showing that the mode of the hotel where spend on advertising average per month is £1460.00. The maximum spends on advertising(£1798.00) are almost 2.5 times of the minimum spending (£651.00).
Descriptive Statistics – numerical variables: Employees
Employees
Mean 19.26470588
Standard Error 0.610356244
Median 18
Mode 15
Standard Deviation 6.164295902
Sample Variance 37.99854397
Kurtosis -0.707479275
Skewness 0.654287392
Range 24
Minimum 10
Maximum 34
Sum 1965
Count 102
Employees frequency
10-12 11
13-15 26
16-18 19
19-21 17
22-24 5
25-27 6
28-30 14
31-33 3
34-36 1
Grand Total 102
The maximum of employees who works in hotel is 34, the minimum of the manpower of the hotel is 10 only. It is different in 3.5 times between in maximum and minimum.
The median is 18 employees and the mode is 15 employees, these two figures are closed.
Descriptive Statistics – numerical variables: Accommodation A
Accommodation type A
Mean 398020.5882
Standard Error 8876.553606
Median 387000
Mode 414000
Standard Deviation 89648.79698
Sample Variance 8036906800
Kurtosis -0.77256128
Skewness 0.260649865
Range 390000
Minimum 253000
Maximum 643000
Sum 40598100
Count 102
Income of Type A frequency
250000-299999 20
300000-349999 12
350000-399999 21
400000-449999 18
450000-499999 15
500000-549999 11
550000-599999 4
600000-650000 1
Grand Total 102
Descriptive Statistics – numerical variables: Accommodation B
Accommodation type B
Mean 212133.3333
Standard Error 729.3568615
Median 211750
Mode 208500
Standard Deviation 7366.143225
Sample Variance 54260066.01
Kurtosis -0.687049798
Skewness 0.262688332
Range 31200
Minimum 198300
Maximum 229500
Sum 21637600
Count 102
Income of Type B frequency
195000-199999 3
200000-204999 15
205000-209999 25
210000-214999 24
215000-219999 17
220000-224999 14
225000-230000 4
Grand Total 102
This table shows the 104 hotels they got the similar on the average monthly income from the accommodation A and B.
Investigate of relationship between Region and Size of Hotel
We are choosing region of the hotel located and the size of the hotel to investigate ant possible association from the categorical variables.
Our hypothesis is set as below:
H_0: No relationship between the room size and the hotel located in country.
H_1: There is a relationship between the room size and the hotel located in country.
According to the data are given from Region and Size of the hotel, we are organizing as the below table:
Size of the Hotel
small medium large
<50 50-100 >100 region
1-FINLAND 13 20 7 40
2-SWEDEN 18 7 8 33
3-NORWAY 14 4 11 29
Total 45 31 26 102
So, base the on above table, we change to the observe value as below table:
Observe value S M L TTL
1-FINLAND 13 20 7 40
2-SWEDEN 18 7 8 33
3-NORWAY 14 4 11 29
Total 45 31 26 102
Then, we start to calculate the expected value, for example,
Expected value S M L TTL
1-FINLAND =40/102*45 =40/102*31 =40/102*26 40
2-SWEDEN =33/102*45 =33/102*31 =33/102*26 33
3-NORWAY =29/102*45 =29/102*31 =29/102*26 29
Total 45 31 26 102
After that, we got the figure as below table
Expected value S M L TTL
1-FINLAND 17.64705882 12.15686275 10.19607843 40
2-SWEDEN 14.55882353 10.02941176 8.411764706 33
3-NORWAY 12.79411765 8.81372549 7.392156863 29
Total 45 31 26 102
The Chi-square test statistics:
O E O-E (〖O-E)〗^2 (〖O-E)〗^2/E
13 17.64705882 -4.647058824 21.59515571 1.22372549
20 12.15686275 7.843137255 61.514802 5.060088552
7 10.19607843 -3.196078431 10.21491734 1.001847662
18 14.55882353 3.441176471 11.8416955 0.813368984
7 10.02941176 -3.029411765 9.17733564 0.915042263
8 8.411764706 -0.411764706 0.169550173 0.020156314
14 12.79411765 1.205882353 1.454152249 0.113657877
4 8.81372549 -4.81372549 23.17195309 2.62907588
11 7.392156863 3.607843137 13.0165321 1.760857128
Total 102 13.53782015
Due to the degree of freedom is = (m-1) (n-1) = (3-1) (3-1) = 4, so that, the critical value of 5% on 4 degree of freedom is 9.488.
Since 13.53782015 is greater than 9.488, we reject H_0.
We conclude that there is a relationship between the room size and the hotel located in country.
Relationship between the total average monthly incomes and distance of the hotel from the nearest rail link
Total we have 102 surveys of hotel, After group the data of total average income and distance of the hotel from the nearest rail link, the figure shown as below table:
x y xy x2 y2
Distance Type A Type B Total income of A + B Column3 Column1 Column2
1 1.5 473000 213000 686000 1029000 2.25 4.70596E+11
2 2.75 263000 198300 461300 1268575 7.5625 2.12798E+11
3 1 423000 212000 635000 635000 1 4.03225E+11
4 2.6 263400 199000 462400 1202240 6.76 2.13814E+11
5 2.4 342000 210500 552500 1326000 5.76 3.05256E+11
6 2.05 363500 206500 570000 1168500 4.2025 3.249E+11
7 0.5 518000 207600 725600 362800 0.25 5.26495E+11
8 1 489300 219500 708800 708800 1 5.02397E+11
9 3.45 281000 204000 485000 1673250 11.9025 2.35225E+11
10 1.2 491000 228500 719500 863400 1.44 5.1768E+11
91 3.7 309600 208100 517700 1915490 13.69 2.68013E+11
92 1.5 496000 218500 714500 1071750 2.25 5.1051E+11
93 3 329000 206000 535000 1605000 9 2.86225E+11
94 2.5 366000 208500 574500 1436250 6.25 3.3005E+11
95 3.5 286100 201700 487800 1707300 12.25 2.37949E+11
96 2.25 286900 202500 489400 1101150 5.0625 2.39512E+11
97 1.25 473000 208400 681400 851750 1.5625 4.64306E+11
98 1.5 537000 217500 754500 1131750 2.25 5.6927E+11
99 2 440000 218700 658700 1317400 4 4.33886E+11
100 2 414000 217000 631000 1262000 4 3.98161E+11
101 2.6 263400 199000 462400 1202240 6.76 2.13814E+11
102 3 446000 212400 658400 1975200 9 4.33491E+11
Sum 248 62235700 144416375 690.105 3.89007E+13
n = 102 Σx = 248 Σy = 62235700 Σxy = 144416375
〖Σx〗^2 = 690.105 〖Σx〗^2 = 3.89E+13
r = (nΣxy-ΣxΣy)/√([nΣx^2-(Σx)^2 ][nΣy^2-(Σy)^2]) nΣxy-ΣxΣy = -703983350
nΣx^2-(Σx)^2 = 8886.71
nΣy^2-(Σy)^2 = 9.46E+13
√([nΣx^2-(Σx)^2 ][nΣy^2-(Σy)^2]) = 916834454
r = -0.76784129
So that, base on the general interpretation of Correlation coefficient, we got the figure is
-0.76784129, that means that there is no relationship between the total average monthly incomes and the distance of the hotel from the nearest rail link.
