Data analysis Essay Example

  • Category:
    Statistics
  • Document type:
    Math Problem
  • Level:
    Undergraduate
  • Page:
    2
  • Words:
    775
  1. 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

  1. 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 H0:

0

Alternative Hypothesis HA:

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 P-values 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.