Econ 1203 - Qmb Project

I. EXECUTIVE SUMMARY CPResorts, established in early 1990s, has been recognised as one of the leading Australia’s resort corporations with several holiday resorts owned and operating across the nation. With the plan to target on different segments, CPResorts Forster, launched in September 2008, has positioned itself as a high-end family resort with associated facilities offered to suit different customers’ needs. These facilities are also projected as the source of revenue above accommodation charges generated within the operation of CPResorts. In the 2009 fast moving and uncertain economic situation, CPResorts Foster report is attempted to examine how successful CPResorts promotion strategies were in stimulating customer activities within 12 months of operation. The analysis is also subjected to serve as the foundation for decision making and further plan development of CPResorts Foster. The main focus is on the use of random sample of 200 families staying in the past 12 months, providing an insights analysis of prospective customers, length of stay and their spending behaviour to draw an inferential conclusion about the efficiency of business operation. Judging criteria will be based on two key performance indicators: a. At least 50% of customers stay in CPResorts Foster for a full week. b. Average daily expense in excess of accommodation costs spent by customer must be at least $260.

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I. FEATURES OF THE DATA SET The distribution of families by number of members in CPResorts Foster has been demonstrated in figure 1.

The highest booking frequency occurs in families with 4 members with 69 out of 200 observations, followed closely by families with 2 members with 67 bookings. Lowest frequency of 20 is found in large families with 5 and 6 people. Proportion of bookings across six length of stay categories has been shown as follow.

In figure 2, length of stay of 200 sampling families in CPResorts Foster ranged from 2 days to 7 days (full week) with 51% of observations have stayed for the full week. Interestingly, following is 38% stayed for only 2 days. The booking age varies from 25 to 64 years of age with a range of 39, which is a considerable large range. However, this is highly a weak dispersion measure as table 1 has shown that the mean and mode are 47 and 37 years of age, respectively. Particularly, the median of 48 obtained from data analysis points out that half of the sample age group are below 48, and half are above 48 years of age. This could help indicate that middle age group are potentially attracted to make the booking in CPResorts Foster. Table 1: Age Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count

47.375 0.66572 4 48 37 9.41475 2 88.6375 6 0.91035 0.08633 39 25 64 9475 200

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The bimodal histogram in figure 3 has shown the distribution of daily expenditure. The larger modal class includes daily spending from $225 to less than $250 while the smaller consists of expenditure from $175 to less than $200 per day. It appears that the frequency drops to the lowest at both ends of the range ($125 to $150 and $450 to $475). This positively skewed histogram indicates a pattern that there is a relatively large number of moderatespending and a small number of heavy-spending customers. Specifically, only 28.5% of the sample spent at least $260 per day on extra facilities. However, further analysis should be taken to obtain enough evidence to test the validity of the sample data. Because CPResorts Foster has considered profit growth as its priority, it would be interested in indentifying which income group as its potential customers. Regression analysis, therefore, would only concern the relationship between income, daily expenditure and length of stay. The records reveal that the income group greater than $60,000 is 138 out of 200, which represent 69% of the total. However, less than 1/3 have the spending level of above $260 per day. To purge the income effect, simple regression method would be employed: Expenditure = β0 + β1 Income + ε The dependent variable is daily expenditure in excess accommodation charges. This is expressed as a function of income, the independent variable which only takes the value of either 0 or 1 (less than or greater than $60,000). This regression will then be used to make a prediction of daily spending on the basis of income. The difference between the observed and predicted expenditure is the error variable ε. As it would be highly impossible to obtain the value of population parameters β0 and β1 in practice, the least square method will be used instead. This involves drawing a straight line in such a way that the total squared differences between the points and the line is minimised. Ŷ = b0 + b1x The relationship between income and expenditure will be described by b0 and b1 with b0 is the intercept between the regression line and y-axis and b1 represents the slope of the line. Regressing the data produces the intercept b0 = 207.12 and b1 = 43.80. As income x is an indicator variable, value of b0 means mean daily expenditure of the below $60,000 income group is $207.12. Value of b1 could be interpreted in a way such that on average, the above $60,000 income group tend to spend $43.80 more than those below $60,000. From table 2, it can be learnt that there is a weak relationship between daily expenditure and income as R-square is only 0.157, which means the model can explain only 15.7% of variation in daily expenditure. As t = 6.09 and p-value = 5.71 x 10-9, which can be approximated as 0, there is overwhelming evidence to infer that two income groups have different mean daily spending. Table 2 Intercept Income

Coefficients 207.1228879 43.80499343

Standard Error 5.972971522 7.190612722

t Stat 34.676691 6.091969506

P-value 4.7256E-86 5.7104E-09

Similar progress will be applied to assess the relationship between income and length of stay. Day = β0 + β1 Income + ε Regression output shows b0 = 2.58 which indicates the below $60,000 income group stay nearly 3 days on average. Value of b1 = 3.19 can be interpreted as those income above $60,000 tend to stay 3 days longer than the below $60,000 group. Page 3 of 6

As the coefficient of determination is 0.3871, this means the model can explain 38.71% of variation in length of stay in CPResorts Foster. As p-value is extremely small which can be approximated as 0, it can be concluded that there are differences between mean length of stay between two income groups. Table 3 Intercept Income

Coefficients 2.58064516 3.19471716

Standard Error 0.237275216 0.285645793

t Stat 10.87617 11.18419

P-value 6.67E-22 8E-23

III. DATA ANALYSIS Random sample is used to obtain evidence to infer the entire population. Therefore, further step is to use hypothesis testing to infer how and to which extent length of stay and spending behaviour can differ in reality. It can be impossible conclude whether the population is normally distributed nor to estimate population variance σ2 . However, according to the Central Limit Theorem (CTL), with a sufficient large sample size of 200, the distribution of the sample mean will be approximately normal. The sample mean, therefore, can be used to estimate the population mean. CPResorts Foster manager believes that the cost of a type I error is relatively high, the significance level is set at 5% consequently. Length of stay analysis The objective of this performance indicator is to describe the population of length of stay in CPResorts Foster. Thus the parameter is the proportion of full week booking. Population proportion p will then be represented by sample proportion p, where p equals 0.51 (51%). The tests are based on the assumption that np ≥ 5 and nq = n(1-p) ≥ 5. As the purpose is to determine whether at least 50% are full week bookings, the alternative hypothesis is H1: p < 0.5 which makes the null hypothesis H0: p ≥ 0.5 The test statistic is z = p- pp(1-p)/n The test is to decide whether there is enough statistical evidence to infer that population proportion p is less than 0.5 (which is the alternative hypothesis). With 5% significance level required, the rejection region is z < -zα = -z0.05 = -1.645 The value of test statistic is z = 0.28. Thus we do not reject the null hypothesis and conclude that there is enough evidence to infer that at least 50% of bookings in CPResorts Foster would be staying for full week. Page 4 of 6

Expenditure analysis The problem objective is to describe the population of the spending above accommodation costs. To conclude that the company has successfully met its performance indicator, mean daily expenditure by customers must be at least $260. Otherwise, CPResorts is not operating efficiently. The alternative hypothesis is set up to express this circumstance H1: μ < 260 The null hypothesis can be expressed as H0: μ ≥ 260 The descriptive analysis has revealed that the sample mean daily expenditure of customers in CPResports x̄ is $237.35 and sample standard deviation s is 51.12. Due to the reason stated earlier, these values will also be used as population mean and population standard deviation. The following question should be addressed: If the sample mean of 237.35 is less than 260, is there enough statistical evidence to allow the manager to confidently infer that the population mean is also less than 260? The rejection method will be used to answer the question above. With α is set at 5%, value of x̄L can be calculated as:

x̄L = μ - zα σ /n = 260 - (1.645)(51.12)/200 = 254.054 Therefore the rejection region is x̄ < 254.054 The sample mean was computed to be 237.35. Because the test statistic is in the rejection region, so the null hypothesis is rejected. In other words, there is sufficient evidence to infer that the average daily spending is less than $260. Consequently, CPResorts Foster has failed to meet the revenue indicator.

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IV. CONCLUSION With the help of statistical data provided, the greater $60,000 income group could be identified as the prospective customers of CPResorts Foster. Both average daily spending level and length of stay of this group are predicted to be greater than the below $60,000 income group. However, income can only explained the variation in daily expenditure and length of stay in a certain extent, especially at a pretty low level for daily spending behaviour. Consequently, to adjust the biasness, CPResorts Foster is advised to refer to other factors to have a better view of its target customers. In addition, the analysis has also raised some concerns about CPResorts Foster business performance in the first year of operation. Although there is enough evidence to infer that at least 50% are full week customers, the expenditure analysis has indicated that their spending level could fall below $260 per day, with sufficient evidence to support. The analysis has provided two important implications. First, with at least 50% are full week customers, this indicates that type and quality of service offered by CPResorts Foster have met customer expectations. This also means that the marketing department has successfully identified customer needs to deliver the right services and add value to its customers. Second, these results also suggest that pricing issue could cause the failure to meet revenue expectation. As income alone cannot fully explain the variation in spending behaviour, high price of services could cause customers to decrease their spending level. Thus, whether high quality – high price can be the best fit strategy for CPResorts Foster, other steps of market research should be undertaken to sufficiently build and maintain the market share in the long run.

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