Estimation of the average price of used car in New South Wales

Question one
Since many buyers wish to purchase a three or four year used car, there is need to estimate the
average price of 2016 and 2017 cars in New South Wales. The descriptive analysis and
confidence level can assist to calculated the sample average prices and estimation the range of
the average population price of used car in new South Wales. The confidence level can be
applied because of the large sample size of 115, thus the central limit theorem applies.
Table 1
The estimated average price of 2016 and 2017 is $ 22071.725 with the minimum price being $
14990 and maximum $ 28950. The average price has high variability as shown by high standard
deviation value of 3635.30. We are 95% confidence that the exact average current price of two or
three used cars in New South Wales lies in the range of $ (22071.725±1162.63).
Question two
Many buyers believe that white cars are safer since they are visible. Therefore, they wish to
purchase white car. This section gives the statistical finding of whether the restricting white cars
will limit buyer’s choice. Testing of the following pair of hypotheses can help us in this case:
H0: The proportion of the white car make and model for sale in in the New South Wales is less
than 30%.
H1: The proportion of the white car make and model for sale in in the New South Wales is less
than 30%.
The binomial test of proportionality out put bellow gives the findings of the analysis.
Table 2

The current estimated proportion of used white cars make and model in NEW South wales is
70%. The p value for the test=0.00 which is less than 0.05, thus Ho is rejected at 95% level of
significance. Therefore, we can conclude that the proportion of used white cars model and make
in New South Wales is more than 30%. Thus, the buyer’s choice is not limited.
Question three
Due to need to know whether the difference exists between prices of cars for sale by privately
and those for sale by car dealers. This section contains the statistical findings that can assist in
determining whether significant difference exists between the two prices. Testing the following
pair of hypotheses can assist in arriving at the finding:
Ho: The prices of cars for sale privately and by car dealers are the same
H1: The prices of cars for sale privately and by car dealers do differ
Two sample assuming unequal variances can be used because there is no population standard
deviation and the box plot which is not included here shows different variability of the two
prices.
Table 3
Even though average Dealer price ($17101.92) is higher than private ($ 14948.94), the difference
between the two is statistically insignificant at 95% level of significance (p value=0.0961) as
shown in the table 3 above.

Question four
This section explores the relationship between price and age of the used car in New South Wales.
Simple linear regression assists in relating the two variables.
Before fitting a linear regression existence of linear relationship between the two and normality
of the error terms should be established. Scatter plot for checking this is as bellow:
Figure 1
Negative linear relationship exists between price and the age of the used car as shown in figure 1
above and the normality plot shows a gradient of 1 and y intercept=0 which implies normal
distribution.
The coefficient of determination and the multiple correlation coefficient are in the table below:
Table 4
Correlation coefficient= 0.887, this shows that there existed strong linear relationship between
price and age of the car which is shown by the scatter plot.
Coefficient of determination=0.787, which gives approximately 78.7%. meaning that 78.7% of
variation in the prices of used cars is explained by variation in the age of the car. The remaining
21.3% of variation is explained by other factors not included in the model.
Table 5