A Random Sample of the Cars Sold in the USA - Research Paper Example

Introduction: This research project aims to analyze the data from a random sample of the cars sold in USA. The data comprises of variables pertainingto Car manufactures, models, prices, MPG (Miles per gallon), engine size, length and weight of the different vehicles. The vehicles are divided into six broad categories; Compact, Small, Midsize, Large, Sporty and Van cars. We will use the inferential statistical methods to analyze the data and deduce conclusions from it. The fundamental objectives of this research include but are not limited to: Compare the mean prices across different vehicle types. Compare the mean MPG (Miles per gallon) across the different categories of vehicles. Test for the difference in mean price of MPG using appropriates statistical methods. Examine the relationship between MPG and other variables in the data set To predict the MPG using appropriate variables Analysis: Basic Price CAR TYPE Compact Small MidSize Large Sporty Van Mean 15.69 8.43 24.11 22.94 16.86 16.2 Standard Error 1.47 0.33 2.16 1.89 2.11 0.68 Median 14.05 8.2 23.05 19.9 13.7 16.6 Standard Deviation 5.87 1.49 10.15 6.26 7.90 2.03 Sample Variance 34.49 2.23 103.07 39.20 62.34 4.11 Kurtosis 0.46 3.05 -0.54 -0.38 1.44 -0.83 Skewness 1.05 1.60 0.69 1.14 1.54 0.51 Range 20.5 6.2 33 16.9 25.5 5.9 Minimum 8.5 6.7 12.4 17.5 9.1 13.6 Maximum 29 12.9 45.4 34.4 34.6 19.5 Count 16 21 22 11 14 9 Confidence Level(95.0%) 3.13 0.68 4.50 4.21 4.56 1.56 Type of Vehicles Compact Compact cars have a mean price of $15,690 with a median price of $14,500. The mean price greater than the median price indicate that most of the prices of compact cars are scattered around smaller values than the mean. A positive skewness of 1.05 also confirms the fact that the distribution is rightly skewed with frequent small values and few extreme values. The sample standard deviation of 5.87 which is quite large shows that on average the compact car prices are $5,870 greater or lesser than the mean price of $15,690. This can be attributed to the fact that most of the compact cars are produced with different qualities and specifications. Furthermore, the brand appeal of different cars is also reinforced in the notion of a large standard deviation in compact cars. Finally, we can be 95% confident that the population mean price of the compact cars ranges from $12,560 to $18,820. Small Small cars have a mean price of $8,430 with a median price of $8,200. The distribution is rightly skewed with a positive skewness of 1.60 which implies that most of the small-sized cars are cheaply priced whereas few of them are expensive. The sample standard deviation of 1.49 shows that on average the compact car prices are $1,490 greater or lesser than the mean price of $8,430. We can infer from this standard deviation that consumers do not differentiate in large when they buy small cars therefore the brand image does not matter as much as it matters in other categories of vehicles. Finally, we can be 95% confident that the population mean price of the small cars ranges from $7,750 to $9,110. Midsize Midsize cars have a mean price of $24,110 with a median price of $23,050. The mean price greater than median price indicates that most of the prices of compact cars are dispersed around smaller values than the mean which can also be confirmed by the fact that the distribution has a positive skewness of 0.69. The sample standard deviation of 10.15 which is extremely large implies that on average the midsize car prices are $10,150 greater or lesser than the mean price of $24,110. We can deduce from this fact that midsize cars are found in number of varieties and consumers have varying tastes for midsize cars. Consumers are willing to pay $45,400 for Infiniti Q45, while at the same time they perceive Hyundai Sunata to be valued at $12,400. This reinforces the concept of strong brand image and differentiation in this segment of vehicles. Finally, we can be 95% confident that the population mean price of the midsize cars ranges from $19,610 to $28,610. Large Large size cars are similar to midsize cars but the only difference evident from the data is the capacity that each car holds. Midsize cars have a capacity to hold 5 passengers whereas large cars can hold up to 6 passengers. Large size cars have a mean price of $22,940 with a median price of $19,900. The distribution has a smallest positive skewness of 0.51 and can be considered as a normal distribution. with frequent small values and few extreme prices. The sample standard deviation of 6.26 which means that on average the midsize car prices are $6,260 greater or lesser than the mean price of $22,940. Again this affirms that we have enormous diversity in this segment of cars. However, there is an interesting fact found in the pattern of data as we have found that the mean price of large cars is lesser than the mean price of midsize cars. According to common intuition, the prices of large cars should be greater than mid size cars so we need to unravel this mystery. Is that difference due to chance or there is a significant difference in the mean prices of both the categories of vehicles. We will conduct a hypothesis test to identify whether these differences are significant or not. Finally, we can be 95% confident that the population mean price of the large cars ranges from $18,730 to $27,150. Sporty Sporty cars have a mean price of $16,830 with a median price of $13,700. The distribution is rightly skewed with a positive skewness of 1.54 which implies that most of the sporty cars are low priced (less than the mean price) whereas few of them are quite expensive. The sample standard deviation of 7.90 reveals that sport cars have a most significant brand appeal with significant differences in the prices. On average the sporty car prices are $7,900 greater or lesser than the mean price of $16,830. Finally, we can be 95% confident that the population mean price of the sporty cars ranges from $12,270 to $21,390. Vans The final category of vehicle from the data set is identified as vans. Vans have the highest passenger capacity and they can hold up to 8 passengers. Vans have a mean price of $16,200 with a median price of $16,600. It is the only data set which has a median value greater than the mean price. The sample standard deviation of 2.03 which is quite small compared to others implies that on average the van car prices are $2,030 greater or lesser than the mean price of $16,200. Lastly, we can be 95% confident that the population mean price of the van cars ranges from $14,640 to $17,760. Top Price CAR TYPE Compact Small MidSize Large Sporty Van Mean 20.73 11.90 30.31 25.67 21.96 22.03 Standard Error 1.99 0.61 3.22 2.01 2.29 1.00 Median 18.50 11.30 27.35 21.90 21.20 21.70 Standard Deviation 7.96 2.80 15.09 6.67 8.57 3.01 Sample Variance 63.38 7.86 227.57 44.47 73.50 9.06 Kurtosis 0.03 0.35 4.55 -0.45 0.66 -1.22 Skewness 0.95 0.92 1.82 0.91 1.03 0.12 Range 25.70 10.90 65.10 19.40 30.50 8.60 Minimum 11.40 7.90 14.90 18.40 11.00 18.00 Maximum 37.10 18.80 80.00 37.80 41.50 26.60 Count 16 21 22 11 14 9 Confidence Level(95.0%) 4.24 1.28 6.69 4.48 4.95 2.31 The pattern of the data is same for Top Price table with the mean prices slightly greater than basic price for all categories of vehicles. The difference in prices is apparent since the top price models have better specifications for the same model of the car. We can individually check for each category of vehicle whether there are significant differences in top and basic price. It is also feasible to conduct an overall hypothesis testing for the differences in top and basic price which can give us a general overview of the scenario. Testing for differences in mean basic price of Midsize and Large Cars MidSize Large Mean 24.11363636 22.93636364 Variance 103.0698052 39.19654545 Observations 22 11 Hypothesized Mean Difference 0 df 29 t Stat 0.409915655 P(T Read More