Part-1

1. Working age population between age 15-64 years:

Central Coast:

The above line chart indicates growth in working age population between 2013 and 2018 in Central Coast Area. It can be seen that the line chart indicates an upward sloping trend in the population over a period of time as seen by the rising blue line in the graph. This means that the working age population between 15-64 years age group is increasing over time. The number was 201,626 in 2013 and increased to 207,306 in 2018. 

North Sydney:

The above line chart indicates growth in working age population between 2013 and 2018 in North Sydney Area. It can be seen that the line chart indicates an upward sloping trend in the population over a period of time as seen by the rising blue line in the graph. This means that the working age population between 15-64 years age group is increasing over time. The number was 51,411 in 2013 and increased to 53,647 in 2018. 

2. Working Population in 2023

For Central Coast, for 2023:

In order to predict the working population, linear regression was performed with output as follows:

According to above, the linear regression equation is: Working population (y) = -2,184,393+1185.286*year (x)

Hence, for x = 2023,

Working Population (y) = -2184393+1185.286*Year

Working Population = -2184393+1185.286*2023 = 213,440.5

For North Sydney, for 2023:

In order to predict the working population, linear regression was performed with output as follows:

According to above, the linear regression equation is: Working population (y) = -892,785+469*year (x)

Hence, for x = 2023,

Working population (y) = -892785 + 469*2023 = 56,002

The regression equation has been formulated for the working population data for both the regions and based on that the prediction/forecast for 2023 has been made. Therefore, the prediction is reliable.

3. Mean Employee Income

The following graphs indicate the mean employee income in Central Coast Area and North Sydney Area for the period of 2013 till 2017:

From the above graphs, it is clear that for Central Coast, the average employee income is increasing over the years. It was $49,706 in 2013 and reached $55,344 in 2017. However, for North Sydney, the average employee income is growing till 2016 but after that, it has become almost stagnant. It was $88,196 in 2013, $100,437 in 2016 and there was negligible increase to $100,491 in 2017.

4. Number of employees:

The following screenshots indicate the number of employees in each of the regions, along with the average and median number of employees also:

Central Coast:

North Sydney:

It can be seen that the minimum and maximum number of employees for Central Coast is 146,556 and 161,585, respectively. The average number of employees during the period of 2013 to 2017 is 154,469.6. The median number of employees during the period of 2013 to 2017 is 156,330.

It can be seen that the minimum and maximum number of employees for North Sydney is 40,069 and 45,658, respectively. The average number of employees during the period of 2013 to 2017 is 43,210.8. The median number of employees during the period of 2013 to 2017 is 44,001.

Part-2

Correlation Tables

North Sydney:

The correlation between the number of business owners and mean total income excluding government pensions and allowances is very high i.e. 0.97. Similarly, the correlation between total number of business owners and mean gross capital gain is 0.99 which is also very high. Almost perfect positive correlation is seen for both.

Central Coast:

The correlation between the number of business owners and mean total income excluding government pensions and allowances is very high i.e. 0.98. Similarly, the correlation between total number of business owners and mean gross capital gain is 0.79 which is also very high. 

The correlation between the number of business owners and mean total income excluding government pensions and allowances is very high for both the regions whereas the correlation between total number of business owners and mean gross capital gain is high for North Sydney as compared to Central Coast.

Part-3:

Probabilities have been calculated by computing the Z scores and then finding the probabilities at various Z scores.

We can see that a very small i.e. almost negligible chance for need to change the tyre in case of Triomphe whereas there is almost 10% change of failure and need to change in case of Palio.

Since the profit margin for Palio is 8% higher than Triomphe but the failure rate is 10% therefore, Tony should proceed with Triomphe brand tyres and sell them more. For Palio he will be facing a loss of 2% because of the excess failure rate.

For 99% confidence interval, Z score = 2.58

X(bar) = Sample mean = 22164

N =60

Assuming the standard deviation for the sample to be 5145 (calculated w.r.t. 6500 for 28000kms).

At 99%, the confidence interval is 20450 to 23878kms.