Statistical Hypothesis Testing and Key Performance Indicators

May 24, 2018 Business

The following report aims to analyse and interpret the data set of 200 records regarding the CCResort. The given information includes booking identification number, income, number of people per booking, length of stay, age and overall expenditure. From the booking ID it can be assumed that the selection of data is random, however as it is only partial information and not the population, the period of time in which the data is selected from would affect the end results of analysis.

The report is divided into two sections outlining the statistical analysis of data and hypothesis testing to observe if CCResort have met their 2 major key performance indicators (KPIs) 1More than 40% of their customers stay for a full week (i. e. seven nights); 2The average customer spends more than $255 per day in excess of accommodation costs. Figures at a glance This section of the report aims to give users a better understanding of the data through statistical data analysis of investigation categories including family income, expenditure habits, age distribution, the number of people per booking and their length of stay.

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These analysis are meaningful in giving users a better understanding of the customer base in relation to the key performance indicators. 1. Family income distribution From the data collected, 62 families (31% of the sample) earn an income of more than $100,000 while 69% of the sample (138 bookings) had income less than $100,000. From the group that had an income of less than $100,000, the average number of people per booking is 3. 2581, the average age of the group is 40. 9032, the average length of stay is 2. 5806 and the average expenditure per day is calculated to be $208.

9798. From the group with income more than $100,000, the average number of people per booking is 3. 6232, the length of stay is 5. 7754, the average age is 48. 0217 and the average expenditure is $248. 3643 per day. 2. Relationship between family income and expenditure The analysis of expenditure is divided into three sections: total expenditure per day, expenditure for bookings with income less than $100,000 and for bookings with income more than $100,000. The total minimum expenditure per day $147 dollars and a maximum of $477. 85.

The average expenditure of the total expenditure per day is $236. 15. For the group with income less than $100,000(62 bookings), the minimum expenditure per day is $147 and the maximum expenditure is $298. 50. The average expenditure for the group is $208. 9798 (approximately $209). The histogram is positively skewed suggesting that there is a negative relationship between expenditure and income. For the group which declared that they have more than $100,000 income (138 bookings), the minimum expenditure per day is $173. 8571 while the maximum expenditure is $477.

The average expenditure for this group is $248. 3643. As seen from the histogram below the data is positively skewed with an outlier, this can be identified as irregular but is not necessarily an error. It can be concluded after analysing the different data that the expenditure is dependent with the income earned where the average daily expenditure for the group with income greater than $100,000 has a higher average expenditure ($248. 3643) in comparison to the group with lower income ($208. 9798). The outlier of $477.

8571 per day should be accounted as it skews the data which may lead to the misrepresentation of the data. 3. Age distribution The age distribution of the sample data is analysed with the following statistical indicators: Mean45. 815 Median45 Mode43 Range36 Standard Deviation9. 76512 Variance95. 35756 Skewness0. 083379 The customers’ age distribution gives CCResort a better understanding of the type of customers has been attracted to the resort by interpretations of the age demographic through the data. The above table shows that the average age of the customers as per booking is 45.

815 at CCResort while the median age is 45. From the data it can be established that younger groups are not the target market of the business. Further analysis of the histogram and the skewness of the data shows that the customers’ age distribution is positively skewed, from which we can conclude that CCResort is visited by families and in general those in the older age groups. 4. Number of people per booking The number of people per booking of the sample data is analysed with the following statistical indicators: Mean3. 51 Median 4 Mode4 Range4

Standard Deviation1. 314741 Variance1. 728543 Skewness0. 333199 The analysis gives the business a general understanding of which type of customers, in groups or as families, it is attracting. From the table above, the average number of people per booking is 3. 51 while the mode and median is 4 which suggest that the resort mainly attracts families usually with 1 to 2 children. Further examination of the data through the histogram as shown below showing that 69 out of the 200 bookings studied, that is 34. 5% of the data is made out of 4 people groups.

Moreover, a total of 33. 5% (67 bookings) of the bookings are made for 2 people which gave an indication that the resort is also popular with couples. In comparing the data set with the age distribution of the customer base, it can be argued that the CCResort mainly attracts families with children as well as couples with no children 5. Length of stay: distribution The length of stay of the sample data is analysed with the following statistical indicators: Mean4. 785 Median7 Mode7 Range5 Standard Deviation2. 380569 Variance5. 667111 Skewness-0. 21356

The statistical analysis of the length of stay is an important indicator as it is one of the key performance indicators of the resort. By observing the table above, the average length of stay for customers at CCResorts is 4. 785 nights with a median of 7 days. The mean and median would however have been strongly affected by the large values at bookings of 2 and 7 night stays showing that the resort is visited on weekends or during longer holidays.

From the histogram below, it is found that the distribution of length of stay is quite bimodal with 75 bookings of 2 days (37.5%) and 102 bookings for 7 day stays (51%) which adds up to a total of 88. 5% of the total bookings. The key performance indicator of having more than 40% of the customers stay for a full week (7 nights) was surpassed since 51% of customers stayed for a full week, it can be concluded that CCResort is performing exceptionally well in relation to its KPIs. Analysing the statistics Testing the Hypothesis 1. At least 40% of our customers stay for a full week (7 nights) The following hypothesis is tested using the binomial approximation method.

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