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Data analysis Essay Example
 Category:Statistics
 Document type:Math Problem
 Level:Undergraduate
 Page:2
 Words:775

Average number of people that local businesses employ in our region
From sample size of the estimate populating, it is evident that the average number of people employed in the local business in the region is approximately 81 people which depict 70% of the population percentage. This population is based in /+ 10% margin of error in our estimates.
Sample size estimate for the 
proportion 
Units of measurement 

Estimate of Population Proportion 

Level of confidence sought 

Margin of error (+/) to detect 

Sample size estimate 

Sample size to obtain (Rounded up) 
81 People 

The proportion of all businesses in the region that do have a growth strategy
On average, the number of business with growth strategy in region is 11.
3 A. Any evidence to suggest that the proportion of local businesses that do have a growth strategy could be less than this suggested figure and thus impacting on revenue in our region?
. To proof this we use standard normal distribution which proofs that the number of business depicts growth strategy in the region greater than the standard deviation from the mean at 10.75 while the number of business with no growth strategy is 0.2506 which is very small. This imply that a high proportion of the local business depict a growth strategy. The impact on the revenue is that the local council will depict a growth as a result of the growth in revenue collection from the growth in local business with growth strategy. (Albright, 2016)Yes there is evident on the share of local business that depicts a growth strategy that might be less than the recommended figure
Standard Normal Distribution 

0 

Standard Deviation (s) 

Value of Variable (x) 

Probability 

P ( x ≤ Standard Deviation (s)) = 

P ( x ≥ Standard Deviation (s)) = 
B. estimate the average number of staff for businesses with and without a growth strategy
The number of staff for business 30.02667. This number is with or without the growth strategy. It can therefore be concluded that the number of businesses with a growth strategy depicts high number of employees on average, and may as a result be more successful? (Black, 2011).
4. A. If the average age of local business managers is indeed less than 50 years
We will use a hypothesis testing

where the null hypothesis is ; the number of local business manager is less than 50

the alternative hypothesis is the number of local business manager is more than 50
Significance level is 95%
Interval estimate is 5%
Hypothesis Test for µ 

Hypotheses 

Null Hypothesis H_{0}: 
0 

Alternative Hypothesis H_{A}: 

Test Type 

Level of significance 

alpha α set to: 

Critical Region 

Degrees of Freedom 

Critical Value 

Sample Data 

Sample Standard Deviation 

Sample Mean x bar 

Sample Size 

Is Pop StDev known? Y/N 

Standard Error of the Mean 

t Sample Statistic 

From our analysis, it is evident that the Pvalues are 1 which more than the significance level and hence, we accept the hypothesis that the average age of managers in Australian businesses is more 50 years.
5. The likelihood that next year:
a. More than 15 businesses will open
We will use the T below to evaluate the number of 15 businesses or more that will open. From T table above, it is evident that the probability that more than 15 businesses will open is 1.75305. This implies that there is high likelihood that much business will open.
b. The number of businesses that open will be 5 or less?
At 5% confident level, we are certain that the probability that five businesses will open is 2.015048. This values is derived from the follw9ng formulae z = (X — μ) / σ where X is a normal random variable, μ is the mean of X, and σ is the standard deviation of X(Robert Stine, 2013).
6. a. Estimate the average number of people that local business employ to within 4 employees
The average number of people that the local business employs to within 4 workers is 50
b. Estimate the percentage of business with a growth strategy to within 2%.
The estimated percentage of business with growth strategy within the range of 2% is estimated to be 70%.
Bibliography
Albright, C. (2016) Business Analytics: Data Analysis & Decision Making — Page 230, London : Cignage Learning.
Black, K. (2011) Business Statistics: For Contemporary Decision Making — Page 296, London.
Palepu, K. (2007) Business Analysis and Valuation: Ifrs Edition — Text Only — Page 11, New York.
Robert Stine, .F. (2013) Statistics for Business: Decision Making and Analysis, New York.
Tufféry, S. (2011) Data Mining and Statistics for Decision Making, New York: Cingage learning.