Further Analysis of Business Confidence and Expectation

This memo outlines the findings from the analysis of sample data on regional businesses, including employment, growth strategies, and more. The analysis reveals insights on average employment, proportion of businesses pursuing growth strategies, average age of managers, and more.

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MEMORANDUM
Date: May 7, 2019
To: Ballarat City Council
From: Nick Black
Subject: Re: Further analysis of Business confidence and expectation
Dear Sir/Mam
I have completed the analysis of the sample data provided with regards to regional businesses. In
this regards, requisite statistical tools have been used based on the information provided and the
nature of question posed. The purpose of this memo is to outline the findings that have emerged
from the analysis of the information provided. These have been presented as follows.
1) The sample data provided indicates that on average 30 employees are employed by each of
the regional business included in the sample. However, the average value does not seem to
provide an accurate indication of the employees employed by each business as it is unduly
influenced by certain businesses which tend to deploy a high number of employees. As a
result, it is better to use the median value as the appropriate representation for average
employment by the sample business. This value is 8 which implies that half or 75 of the
businesses included in the sample tend to employ 8 or less employees. The minimum
employee employed by a regional business included in the sample data is 1 while the
maximum value is 308. This clearly represents that the extent of dispersion or variation that
is witnessed with regards to number of employees for the sample firms is quite high. Further,
the distribution of employees in sample firms seems to be quite skewed as majority of the
firms tend to have low count of employees (8 or below) but there are certain firms in the
sample which have quite a high number of employees thereby having a distorting impact on
the sample data.
2) The objective was to estimate the proportion of businesses in the region which have agrwoth
strategy in place. The estimation for all the regional businesses located in the Ballarat City
has been made using the sample data provided. It can be estimated that of all the regional
businesses in Ballarat City, the proportion of those which are pursuing a growth strategy
would lie between 64.10% and 78.57%. However, it is noteworthy that there is a 5% chance
that the above proportion may not lie in the interval estimated above. For more accuracy in
estimation, a wider interval would be recommended. Also, based on the estimate, it is
appropriate to conclude that regional businesses seem confident about the business prospects
going forward owing to which a majority of regional businesses are pursuing growth
strategy.
3) As per the claim from Clunes Chamber of Commerce, it is imperative that 76% regional
businesses should pursue a growth strategy or else the regional revenue would suffer
significantly. Based on the sample data for regional businesses in Ballarat City, the above
claim has been checked so as to outline if this is a matter of concern that needs attention of
the council or not. The result suggests that the proportion of regional businesses located in

Ballarat City which are pursuing growth strategy do not seem to be lower than 76%. As a
result, this is not a matter of concern.
Further, an estimation of the average number of employees by regional business pursing growth
strategy and non-growth strategy has been made in an attempt to ascertain if businesses having a
growth strategy on average tend to have more employees than those which do not pursue growth
strategy. The average employee strength for regional businesses with growth strategy is
estimated to lie between 25.40 and 44.07. In comparison, the average employee strength for
regional businesses without growth strategy is estimated to lie between 11.75 and 24.86. Clearly,
the two do not overlap which implies that average employees for regional businesses with
growth strategy on average tends to be higher than those regional businesses without growth
strategy.
4) The objective is to analyse if the average age of managers in regional businesses tends to less
than the Australian average of 50 years or not. The sample data provided does not support the
claim made by you. This is because it cannot be concluded that the average age of managers
for regional businesses in Ballarat city is lower than 50. As a result, it may be concluded that
the age trend of business managers exhibited by regional businesses in the Ballarat region do
not differ from the national trends.
5) Based on the historical trends, it is known that on average 10 businesses open in an year.
Taking this as the average performance, it can be estimated that the probability associated
with the opening of more than 15 businesses is expected to be 0.0487. As a result, it can be
concluded that happening of such an event is quite unlikely. On the other hand, the
probability of opening of 5 or less business is also quite slim as it is estimated to be 0.0671.
Thereby, it seems reasonable to say that the new businesses that would open annually in the
Ballarat city would lie between 5 and 15 with an average of10.
6) The objective of the analysis was to compute the requisite sample size in the wake of specific
tasks that you wanted to perform based on the given accuracy standards. In order to estimate
the average employees hired by regional business within a 4 employee margin of error, the
minimum sample size is 697. Further for estimation of proportion of businesses pursuing a
growth strategy within 2% margin of error, the minimum sample size required is 1964.
Considering that you want to accomplish both, hence the sample size to be selected next year
should comprise of atleast 1,964 regional businesses.
In case of any further queries or follow up questions, please do not hesitate to contact me.
Yours Sincerely
Nick Black