Foundation Skills in Data Analysis

This memo provides answers to queries related to statistical analysis of sample data on local businesses in Bellarat City. It discusses the average number of employees, growth strategies, age of managers, and probabilities of new businesses opening. It also mentions the minimum sample size for estimating average employee count and businesses with growth strategy.

FOUNDATION SKILLS IN DATA ANALYSIS
STUDENT ID:
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MEMORANDUM
Dear Sir/Madam
The objective of this memo is to provide answers in the context of the various queries that have
been forwarded in the email. In responding to these queries, statistical analysis has been
conducted based on the sample data that has been provided. This sample data comprises of
information with regards to 150 businesses that are situated locally within the Bellarat City.
Appropriate statistical measures and tools have been deployed so as to carry out analysis of the
data presented in the wake of the queries raised. The findings from this analysis in the context of
queries posed have been presented in brief below.
1) Considering the sample mean, it can be stated that each of the business that is part of the
sample tends to employ 30 employees on an average. But when the median value of
employees from the sample data is derived, it arrives significantly lower at only 8 employees.
The significant difference between the median and mean values may be the result of presence
of certain local businesses in the sample which employ a large number of people. This has
therefore led to the mean value being skewed but the median is not influenced by these
extreme values and thereby presents a more accurate picture. Hence, the average number of
employees for each of the sample business would be considered as 8 as 50% of the
observations (i.e. 75 businesses) have employee strength which is not exceeding 8. It is
imperative to understand that some of the large regional businesses which have high number
of employees do not provide a realistic example of businesses located in the area as most of
the businesses are typically small and do no employ high number of employees. Further, the
amount of dispersion in the employee variable for the sample data is high as the lowest value
is 1 as compared to the maximum value of 308. The presence of high values clearly
illustrates that the employee variable is skewed as abnormally large values seem to be
present. The presence of these local businesses, which have abnormally high employee
count tend to produce distortion in the data and various sample statistical measures.
2) The sample data furnished has been used to ascertain the percentage of all local businesses
within the Ballarat city that are following a growth strategy. The application of relevant
statistical technique reveals that the between 64.10% and 78.57% of all local businesses have
a growth strategy which is being followed. The estimate provided in not 100% accurate as
there is a 5% possibility that the actual proportion for the population data may not lie within
the interval defined above. Based on this healthy proportion, it can be inferred that the extent
of business confidence with regards to future for local businesses seem to be quite optimistic
as growth strategy would be expected to be pursued during period of robust economic growth
and not during a downturn.

3) In accordance with the claim by a leading professional body, failure in regards to atleast 76%
of the local businesses following a growth strategy could severely dent the revenues and
thereby have an adverse impact on the financial stability. The given claim has been checked
for the given sample data so as to estimate if proportion of all local businesses in Ballarat city
that tend to adhere to a growth strategy are significantly lower than 76%. The available
evidence from the statistical analysis of the sample data does not indicate the same and
thereby the financial concerns are unlikely to arise.
Further, in context of the local or regional businesses, it needed to be tested if the average
employee count in firm with growth strategy tends to be significantly higher than the
corresponding employee count for firms without growth strategy. The average employee strength
for all local businesses that have a growth strategy is estimated in the interval (25.40,44.07). In
comparison, the average employee strength for all local businesses that do not have a growth
strategy is estimated in the interval (11.75,24.86). The two intervals representing estimation of
mean employees for firms based on presence or absence of growth strategy do not overlap which
clearly hints towards existence of sizable difference. As a result, the sample data of 150
businesses provided supports the claim of firms with growth strategy employing higher count of
employees on average then firms where the growth strategy is absent.
4) A claim made by the city council is that the local businesses tend to deploy younger
managers as compared to the national trends. As a result, using the sample data, suitable test
has been performed to ascertain if support is available for this claim. However, the results
obtained clearly highlight that the claim made by the council about the managers being
younger is not supported. Therefore,, it would be suitable to conclude that in terms of age of
managers, the trends in local businesses are similar to that seen for Australia as a whole.
5) It is known that 10 new businesses open on an annual basis on average in Ballarat city. Using
these information, it can be estimated that the requisite probability of more than 15
businesses opening in the city in one year would be quite low at 0.0487. With regards to the
opening up of not more than 5 businesses in a given year, the corresponding probability Is a
little higher at 0.0671.
6) There is requirement of a minimum sample size of 697 local businesses if you want to
estimate the average employee in a local business with the stated MOE (Margin of Error) of
4 employees. However, this sample size is not sufficient to estimate the local businesses
proportion with growth strategy with the stated MOE of 2%. For this, the minimum sample
size would comprise of 1.964 local businesses. Hence, if the council desires to satisfy both
the requirements, then the minimum sample size selected should be 1.964.
For any further doubts or clarifications, you can contact me through over email.
Yours faithfully
Nick Black