Foundation Skills in Data Analysis (MIS770) Assignment 2 Report

This report, prepared for the MIS770 course, analyzes data from 150 local and regional businesses to address questions about employee numbers, growth strategies, and business confidence in the Ballarat City area. The analysis includes calculating average and median employee counts, estimating the proportion of businesses with growth strategies, assessing revenue implications, and comparing manager ages to national averages. Statistical methods are used to determine confidence intervals and probabilities related to business openings and employee strength. The report concludes with recommendations on sample sizes for future data collection, aiming to provide a comprehensive overview of the regional business landscape and address concerns about revenue and business confidence. The findings support that most businesses have a growth strategy, and that employee numbers are linked to the presence of a growth strategy.

FOUNDATION SKILLS IN DATA ANALYSIS
STUDENT ID:
[Pick the date]

MEMORANDUM
Dear Sir/Madam
The given memo aims to answer the questions that were posed by your email pertaining to
various aspects of regional businesses. The sample data comprising of information about 150
local/regional businesses has been used along with requisite statistical methods to provide
accurate responses. A summary of the key findings in the context of the various questions posed
are mentioned as follows.
1) The key objective was to provide an overview of the employees that are employed by the
local or regional businesses that are present in the sample. The average value for the sample
data indicates that every firm in the sample on average provides employment to 30
employees. This clearly is inaccurate summary of the sample as the average value is
influenced by certain businesses that have a large workforce and thereby is distorting the
mean performance in terms of employee strength. In wake of these extreme values, a more
prudent approach would be to rely on the median value which is not impacted by the
incidence of abnormally high or low values. The median employees hired by the sample local
business are 8 which represents that 75 of the sample businesses do not employ more than
this count of employees. It would be appropriate to take this as the average number as some
of the businesses included in the sample do not provide an accurate representation of the
local businesses in Ballarat City. The employee count across the various local businesses
exhibits high dispersion which is quite visible from the high range since there is a business
which provides employment to 308 people while at the other extreme, there is another
business which provides employment to only 1 person. Therefore, it can be concluded that
presence of some big local businesses is essentially distorting the statistics related to sample
and hence suitable measures should be used to summarise the sample characteristics.
2) The objective of this analysis was to draw an estimate of proportion of all local or regional
businesses which are situation in Ballarat city and have a growth strategy. Taking into
consideration the sample data and requisite statistical technique, this interval has been
estimated with the boundaries on lower and upper end being 64.10% and 78.57%. The actual
proportion is expected to lie in the above interval with 95% chance which implies that there
is 5% chance of the above interval not capturing the given variable. Considering that both
the limits are well above 50%, it clearly provides indication of the high business confidence
that seem to be prevailing with regards to the future performance based on which a majority
of the regional businesses have a growth strategy.

3) There are concerns that if at a minimum 76% of all the regional businesses do not have a
growth strategy, then potentially the revenues would take a severe hit which could have
implications for the business confidence. The sample data for the regional businesses based
in Ballarat city provide indications that the businesses do not deviate from the 76% figure in
any significant manner. As a result, the revenues for the city should not be a concerning
issue and also the business confidence going forward should be good.
Also, given the sample data , it needs to be checked if the regional businesses that have a growth
strategy tend to deploy higher number of people on average when compared to the regional
businesses lacking growth strategy. For the local businesses where growth strategy does exist,
the employee strength on average ranges from 25.40 to 44.07. Foe the local businesses, where
growth strategy does not exist, the employee strength on average range from 11.75 to 24.86. For
the two different categories of local businesses, it is evident that there is no overlap in the
estimated intervals. This clearly provides concrete evidence of difference in employees in the
two categories of firm with more employees expected in the category with the larger value of the
interval. Therefore, the sample data provides support to the claim.
4) The city council is of the opinion that the average age of managers at the local businesses is
lesser than elsewhere in Australia. This belief has been tested using the sample data in
regards to the age of the managers and the same is compared to the corresponding national
average of 50 years. The requisite statistical analysis fails to show any meaningful difference
between the average managers age for local businesses in Ballarat city and Australia.
Thereby, it would be apt to opine that the belief held by the council is not supported by the
sample data and probably incorrect.
5) The given data highlights that on an average every year 10 local businesses are set up. This
information has been deployed using suitable statistical methods to estimate that there is a
probability of 0.0487 that more than 15 businesses would open in a particular year. However,
the probability that in a given year, no more than five businesses has been computed as
0.0671.
6) For estimation of employee strength on average in the local businesses with an estimated
error margin of only 4 employees, the sample size required need to be 697 at the least. For
the other estimation i.e. proportion of local businesses where growth strategy does exist with
an error margin of 2%, the above estimated sample size was not found sufficient. In order to
ensure that this condition is fulfilled, 1,964 observations should be atleast included in the
sample for the next year.
In case of any more queries or follow-up questions relating to this memo or analysis conducted,
feel free to reach me over email.
Yours faithfully
Nick Black