Types of Car Markets | HowStuffWorks

Introduction 

Two types of car markets are domestic and foreign. The study aims to assess the two types of cars using descriptive statistics. The domestic and foreign car is explained by three variables , that is the list price, sale price and the days for sale. A sample of 200 cars was collected and categorized based on the market type. Each category ha s three variables that are continuous and comprise o f the list price measured in thousand dollars, sale price in thousand dollars and the days for sale.  

Overview of all Domestic Cars 

In this category, a sample of 200 cars was taken with three variables that are the list price, sale price and the days for sale. Descriptive statistics approach was employed , comprising of the measures of centrality and dispersion. The cars have an average list price of $ 33,161.50 . It had a range of $ 75,000 with a maximum list price of $ 78,800 and a minimum list price of $ 3800. The medium is $ 29,550. Further, the average sale price for the cars is $29,743 with a standard deviation of $ 18,250.88. The medium is $27,5500with a range of $74,600 that has a maximum sale price of $74,600 and a minimum of $1900. The average number of selling days is 32.905 and a standard deviation of 17.86 days. With a medium of 31 days and a range of 69 days having a maximum of 70 selling days and minimum 1 sell day. The z-score indicated that there are no outliers in the dataset. The data set is summarized below in Table 1. 

Table 1 : Descriptive Statistics for All Domestic Cars 

List Price in K		Sale Price in K		Days to Sell
Mean	32.1615	Mean	29.743	Mean	32.905
Median	29.55	Median	27.55	Median	31
Standard Deviation	18.31094	Standard Deviation	18.25088	Standard Deviation	17.86735
Range	75	Range	74.6	Range	69
Minimum	3.8	Minimum	1.9	Minimum	1
Maximum	78.8	Maximum	76.5	Maximum	70

Overview of All Foreign Cars 

A sample of 200 cars was taken with three variables that are the list price, sale price and the days for sale. Descriptive statistics was employed comprising of the measures of centrality and dispersion ( Bonner, 2018) . The cars have an average list price of $ 48,655.50 with a standard deviation of $ 25,455.40. It had a range of $ 88,400 with a maximum list price of $ 89,500 and a minimum list price of $ 1100. The medium is $ 50,050. The average sale price for the cars is 46, 207 with a standard deviation of $ 25,450. The medium is $48,850 with a range of $87,200 that has a maximum sale price of $88,000 and a minimum $800. The average number of selling days is 35.14 and a standard deviation of 19.15 days. With a medium of 34 days and a range of 99 days having a maximum of 100 selling days and minimum 1 sell day. The z-score indicated that there are no outliers in the dataset. The data set is summarized below in Table 2. 

Table 2 :Descriptive Statistics for All Foreign Cars 

List Price in K		Sale Price in K		Days to Sell
Mean	48.6555	Mean	46.207	Mean	35.14
Median	50.05	Median	48.85	Median	34
Standard Deviation	25.4554	Standard Deviation	25.45091	Standard Deviation	19.15843
Range	88.4	Range	87.2	Range	99
Minimum	1.1	Minimum	0.8	Minimum	1
Maximum	89.5	Maximum	88	Maximum	100

Table 1 and 2 shows the descriptive statistics of domestic and foreign cars. For foreign cars, the average list price is $ 48,637 and the mean sale price is $ 46,195 that is higher compared to the domestic cars. Domestic cars have an average list price of $ 32,388 and a sale price of $ 29,969. This suggests that foreign cars are at a higher price compared to the domestic ones. In addition, foreign care takes 35 days to be sold relatively higher compared to the domestic ones. This shows that people buy domestic cars more often compared to foreign cars. The confidence interval between two different means will be useful to obtain additional information about car sales. Because it estimates the difference in the number and prices of cars soles between domestic and foreign cars, and the confidence interval. Thus, when the level of confidence is increasing, it widens the interval. 

Confidence Interval for Sales Price and Number of Days to Sell Domestic Cars 

Table 3 : Confidence interval for domestic o n cars 

Descriptive statistics
	Sale Price in K	Days to Sell
Count	200	200
Mean	30.745	38.44
confidence interval 98.% lower	27.943	35.14
confidence interval 98.% upper	33.546	41.74
margin of error	2.801	3.30
Z	2.326	2.326

Based on the above output, the z-score for the sale price of domestic cars is 2.326 with a marginal error of 2.801. The sale price of the cars lies between $ 27,943 and $ 33,546 at 98 % confidence interval. This implies that we are 98 percent confident that the sale price for domestic cars will range from $ 27,943 to $ 33,546. Further, the z-score for the number of days a car is sold is 2.326 with a marginal error of 3.30. At 98 percent confidence interval, the number of days domestic cars are sold ranges from 35.14 to 41.74. Implying that we are 98 percent that the sell days are between 35.14 to 41.74 days. 

Confidence Interval for Sales Price and Number of Days to Sell Foreign Cars 

Descriptive statistics
	Sale Price in K	Days to Sell
Count	200	200
Mean	39.585	45.46
confidence interval 98.% lower	35.667	41.26
confidence interval 98.% upper	43.502	49.65
margin of error	3.917	4.20
Z	2.326	2.326

Table 4 : Confidence interval for foreign cars 

The table shows the confidence interval for the sales price and sells days for foreign cars. The mean for sales price is 39.585 with a 98 percent confidence interval ranging from $ 35,667 and $ 39,585. Its z-score is 2.326 with a marginal error of 3.917. On the other hand, the average number of days a foreign car is sold is 45.56 a with a 98 percent confidence interval lying between 41.26 and 49.65 days. Hence, the upper limit is 49.65 days and the lower limit is 41.26 days. 

Margin error = z * 

Where is the z- score, n is the sample size and  is the standard deviation . 

For domestic cars 

Margin error = 7 days. At 98 confidence level the z-score = 2.326. 

7 = 2.326 * 

3.01= 

 = 20.05/3.01 

 = 6.66 

n=44.3 

= 45 cars 

For Foreign cars 

Margin error = 8 days. At 98 confidence level the z-score = 2.326. 

7 = 2.326 * 

3.01= 

 = 25.51/3.01 

 = 8.48 

n=71.91 

= 72 cars 

Sample size formulae is very important is it helps us to estimate the marginal error between various different types of car businesses ( Chatfield, 2018) . The advantage of having a large sample size is that it provides more accurate values, identifies the outliers and provide s a smaller margin of error ( Mendenhall et al., 2016) . 

For the Foreign cars , we predict the selling price based on the number of sell days . W e use the regression equation below . 

Sale price = -2.53 +1.0005 List price 

Given the list price is $30,000 

Sale price = -2.53+ 30.015 

= 27.485 

Thus , the sale price will be $27,485. 

Predicting the number of sells days we employ the following regression equation, 

Days = 42.735 +0.0646 List price 

Since, list price = 30 

Days = 42.735 + 1.938 

= 44.673 

Hence, the number of days to sell the cars is 44.673 days. 

For the domestic cars, the sales price can be predicted using the following regression equation. 

Sale price = -2.06 +0.9891 List price 

G iven the list price is $30,000. 

Sale price = -2.060+29.67 

= 27.61 

The sale price will be $27,610 

Predicting the number of sells days we employ the following regression equation, 

List price = 30.0. 

Days = 38.35 +0.0028 List price 

Days = 38.35 + 0.084 

= 38.43 

The number of days to sell the cars is 38.43 days. 

Conclusion 

The main aim of the study is to examine both domestic and foreign cars. A sample of 200 cars was taken based on the list price, sale price and a number of sell days. It was established that the list and sale price for domestic cars is lower compared to that of foreign cars. Further, domestic cars were old and more frequent compared to foreign ones. The domestic cars are less costly and are more preferred compared to the foreign ones. A list price of $30,000 for the domestic cars has an estimate of $27610 sale price and 38.43 days. Given that the list price is $30,000 the estimated sale price is $27,485 and 44.67 sell days. 

References 

Bonner, M. D. (2018). Descriptive statistics.  Police Abuse in Contemporary Democracies , 257. 

Chatfield, C. (2018).  Statistics for technology: a course in applied statistics . Routledge. 

Mendenhall, W. M., Sincich, T. L., & Boudreau, N. S. (2016).  Statistics for Engineering and the Sciences, Student Solutions Manual . Chapman and Hall/CRC.