# Statistics Report

**Topics:**Arithmetic mean, Statistical hypothesis testing, Statistics

**Pages:**6 (1446 words)

**Published:**June 1, 2013

Strategic analysis

business analytics department for CCResorts Central coast

Strategic analysis

BUsiness analytics Department

Executive summary

This study was produced on behalf of the Business Analytics Department at DGHG for CCResorts in order to examine market research and determine how the venture is progressing. The company provided a data sample from the past 12 months with 200 entries, each with 6 variables. The aim of this report is to evaluate the success of CCResorts in fulfilling their key performance indicators as outlined in their business plan, determines the clientele that are attracted to CCResorts and analyses the effect of different variables on the expected expenditure of the customers. The statistical analysis yielded several significant conclusions discussed in terms of their implications for CCResorts. The sample meets with key performance indicator 1 with over 40% of guests staying the full week. There is sufficient evidence to suggest that over 40% of the total population also stay 7 days at CCResorts. On average, majority of customers do not spend more than $255 per day at the resort. Despite this, there are certain demographics that are more likely to achieve a higher expenditure per day. Firstly, the age of the guest impacted their daily expenditure with customers who were older tending to spend slightly more than their younger counterparts. Furthermore, guests who stayed in large groups had a greater likelihood of fulfilling the second key performance indicator. Customers with an income over $100 000 p.a were more inclined to spend more money in excess of accommodation costs.

introduction

The central focus of this statistical report is to determine the success of CCResorts in achieving their key performance indicator (KPI) goals. Ultimately, in order to measure these successes the analysis should focus on determining the percentage of customers who stay a full week and whether or not the average customer spends more than $255 per day in excess of accommodation costs. In addition to this, the characteristics of the average customer at CCResorts and the size of party per booking must be explored. An analysis of the statistical data provided by the resort will outline the various characteristics of customers that affect their expected expenditure, as well as providing recommendations of how to better meet the KPIs.In order to do so, we begin by evaluating the success of CCResorts in meeting their KPIs.

key performance indicators

1. Length of stay – do more than 40% of customers stay a full week? Figure 1: Frequency distribution of days stayed at CCResorts From Figure 1, the mode is 7 days stayed having a frequency of 102. Initially, it seems the first key performance indicator has been achieved with 51% of guest in the sample staying full a full week and the median being 7. However, we cannot assume that this sample if reflective of the entire population. To counter this problem a single tailed hypothesis test at a confidence level of 95% must be conducted to ensure CCResorts has met their key performance indicator.

Central Limit Theorem can be invoked in this case since the sample size is large (n≥30) and we can assume there is a normal sampling distribution.

H0: p = 0.4, H1: p > 0.4, n = 200, p̂ = 0.51, α=0.05

Using the z table, the Z value for the 95% significance level is found in order to determine the rejection region.

Z0.05 = 1.645

Find the value for Z

Z=p̂-pp(1-p)n

1.645

0

Z

Reject

1.645

0

Z

Reject

0.05

0.05

=0.51-0.40.4(1-0.4)200

0.05

0.05

=0.110.24200

=3.17542…

≈3.175 (3 d.p)

Since, Z = 3.175 > Z0.05

3.175 > 1.645

The z-value is greater than the rejection region; we can reject the null hypothesis (H0) and conclude that more than 40% of all customers stay at CCResorts for a full week.

Key Performance indicators

2. daily expenditure – does the average customer spend...

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