When looking at the numerical variables rnd_adj_fe (MPG), rated_horsepower (HP), and equivalent_test_weight_lbs (Weight) means across vehicle types and transmission types differed based on several factors. One of the main factors that could lead to varied results is sample size per groups. For example looking at Automated Manual - Selectable for Car it gave a mean MPG as 32.64 with a sample of 39. When comparing it to Trucks for the same transmission type MPG was slightly higher at 37.95 MPG with a sample size of 13. Previous analysis showed us that Trucks tend to be less fuel efficient than Cars but perhaps Automated Manual - Selectable could lead to trucks being more fuel efficient.
When looking at Semi-Automatic vehicles and comparing Cars to Trucks with a large sample size we can see in this instance Cars get better MPG on average. Cars had 31.65 MPG on average while Trucks had 27.16 MPG with sample sizes of 61 and 93 respectively. These large sample sizes would tell us the samples for transmission and vehicle type would represent a normal distribution allowing for a more likely estimate towards the population mean.
Another comparison between Trucks and Cars could be seen for Automatic transmission type with sample sizes of 69 and 32 respectively. There was a fairly large difference in weight between the two vehicles with Cars having a weight of 4335.94lbs and Trucks average weight being 5184.78lbs. A surprise in this comparison is even though sample sizes were above 30 HP was greater for Automatic Cars 330.5 compared to Trucks 317.74. This could be due to outliers in Automatic Cars in the data set that have a significantly higher HP than Automatic Trucks do.
## vehicle_type: Both
## tested_transmission_type: Automated Manual
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 2.0000 2.0000 2.00000
## mean 406.0000 4750.0000 30.35000
## stdev 261.6295 707.1068 17.04127
## min 221.0000 4250.0000 18.30000
## max 591.0000 5250.0000 42.40000
## ------------------------------------------------------------
## vehicle_type: Car
## tested_transmission_type: Automated Manual
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 12.0000 12.0000 12.0000
## mean 629.4167 4145.8333 24.2500
## stdev 220.7291 340.5933 10.3319
## min 221.0000 3750.0000 14.4000
## max 823.0000 5000.0000 52.1000
## ------------------------------------------------------------
## vehicle_type: Truck
## tested_transmission_type: Automated Manual
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 1 1 1.0
## mean 500 5500 14.7
## stdev NA NA NA
## min 500 5500 14.7
## max 500 5500 14.7
## ------------------------------------------------------------
## vehicle_type: Both
## tested_transmission_type: Automated Manual- Selectable (e.g. Automated Manual with paddles)
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 8.00000 8.0000 8.00000
## mean 232.87500 4140.6250 33.58750
## stdev 31.94834 397.7476 9.58249
## min 189.00000 3500.0000 23.30000
## max 261.00000 4500.0000 51.30000
## ------------------------------------------------------------
## vehicle_type: Car
## tested_transmission_type: Automated Manual- Selectable (e.g. Automated Manual with paddles)
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 39.0000 39.0000 39.00000
## mean 366.5385 4384.6154 32.64359
## stdev 242.9766 822.3765 10.73668
## min 104.0000 3250.0000 15.10000
## max 1500.0000 6000.0000 68.20000
## ------------------------------------------------------------
## vehicle_type: Truck
## tested_transmission_type: Automated Manual- Selectable (e.g. Automated Manual with paddles)
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 13.0000 13.0000 13.000000
## mean 244.8462 4471.1538 37.953846
## stdev 83.2855 346.6876 7.256907
## min 177.0000 3875.0000 27.300000
## max 434.0000 5000.0000 48.500000
## ------------------------------------------------------------
## vehicle_type: Both
## tested_transmission_type: Automatic
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 26.0000 26.0000 26.00000
## mean 345.3846 4490.3846 32.16923
## stdev 135.9597 530.2394 10.71742
## min 202.0000 3750.0000 16.60000
## max 707.0000 5500.0000 50.40000
## ------------------------------------------------------------
## vehicle_type: Car
## tested_transmission_type: Automatic
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 78.0000 78.0000 78.00000
## mean 370.4744 4772.4359 68.58718
## stdev 142.6993 709.0394 50.05035
## min 37.0000 3500.0000 17.10000
## max 693.0000 6000.0000 185.30000
## ------------------------------------------------------------
## vehicle_type: Truck
## tested_transmission_type: Automatic
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 87.0000 87.0000 87.00000
## mean 318.4943 5247.1264 49.75862
## stdev 118.6153 840.2521 43.65365
## min 98.0000 3625.0000 14.90000
## max 657.0000 6500.0000 169.00000
## ------------------------------------------------------------
## vehicle_type: Both
## tested_transmission_type: Continuously Variable
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 1 1 1.0
## mean 176 4000 49.1
## stdev NA NA NA
## min 176 4000 49.1
## max 176 4000 49.1
## ------------------------------------------------------------
## vehicle_type: Car
## tested_transmission_type: Continuously Variable
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 27.00000 27.0000 27.00000
## mean 167.25926 3629.6296 52.20000
## stdev 52.32119 586.7953 25.93938
## min 78.00000 2500.0000 24.30000
## max 295.00000 5500.0000 149.80000
## ------------------------------------------------------------
## vehicle_type: Truck
## tested_transmission_type: Continuously Variable
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 12.00000 12.0000 12.000000
## mean 173.83333 4562.5000 41.733333
## stdev 19.58586 371.1928 9.207441
## min 137.00000 4000.0000 31.000000
## max 189.00000 5000.0000 55.100000
## ------------------------------------------------------------
## vehicle_type: Both
## tested_transmission_type: Manual
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 1 1 1.0
## mean 228 3625 27.6
## stdev NA NA NA
## min 228 3625 27.6
## max 228 3625 27.6
## ------------------------------------------------------------
## vehicle_type: Car
## tested_transmission_type: Manual
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 19.0000 19.000 19.00000
## mean 241.7368 3407.895 37.65789
## stdev 134.2282 372.310 11.79333
## min 134.0000 3000.000 15.30000
## max 668.0000 4500.000 56.30000
## ------------------------------------------------------------
## vehicle_type: Truck
## tested_transmission_type: Manual
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 2.000000 2.0000 2.00000
## mean 281.500000 4875.0000 24.05000
## stdev 4.949747 176.7767 5.16188
## min 278.000000 4750.0000 20.40000
## max 285.000000 5000.0000 27.70000
## ------------------------------------------------------------
## vehicle_type: Both
## tested_transmission_type: Other
## NULL
## ------------------------------------------------------------
## vehicle_type: Car
## tested_transmission_type: Other
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 19.0000 19.0000 19.00000
## mean 436.5263 5006.5789 106.18421
## stdev 237.2976 437.9436 48.92172
## min 147.0000 3875.0000 25.60000
## max 925.0000 5500.0000 149.90000
## ------------------------------------------------------------
## vehicle_type: Truck
## tested_transmission_type: Other
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 9.00000 9.0000 9.000000
## mean 392.22222 5944.4444 110.677778
## stdev 62.77893 747.6816 9.678556
## min 295.00000 5250.0000 98.700000
## max 496.00000 7000.0000 127.700000
## ------------------------------------------------------------
## vehicle_type: Both
## tested_transmission_type: Selectable Continuously Variable (e.g. CVT with paddles)
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 8.00000 8.0000 8.000000
## mean 197.75000 3843.7500 37.025000
## stdev 39.79142 256.6091 7.755689
## min 152.00000 3500.0000 27.200000
## max 260.00000 4250.0000 48.400000
## ------------------------------------------------------------
## vehicle_type: Car
## tested_transmission_type: Selectable Continuously Variable (e.g. CVT with paddles)
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 14.00000 14.0000 14.000000
## mean 214.64286 3776.7857 37.778571
## stdev 64.28615 537.4856 9.419144
## min 120.00000 3000.0000 25.600000
## max 300.00000 4500.0000 57.800000
## ------------------------------------------------------------
## vehicle_type: Truck
## tested_transmission_type: Selectable Continuously Variable (e.g. CVT with paddles)
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 25.00000 25.0000 25.00000
## mean 202.60000 3990.0000 39.47200
## stdev 44.38187 366.0743 10.07375
## min 147.00000 3250.0000 23.70000
## max 268.00000 5000.0000 56.40000
## ------------------------------------------------------------
## vehicle_type: Both
## tested_transmission_type: Semi-Automatic
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 78.0000 78.0000 78.000000
## mean 337.6538 4599.3590 32.785897
## stdev 130.9803 530.8498 8.855517
## min 164.0000 3750.0000 13.400000
## max 617.0000 6000.0000 49.400000
## ------------------------------------------------------------
## vehicle_type: Car
## tested_transmission_type: Semi-Automatic
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 61.000 61.0000 61.000000
## mean 407.623 4336.0656 31.649180
## stdev 197.557 662.0443 9.744958
## min 134.000 3250.0000 10.600000
## max 1500.000 6500.0000 59.800000
## ------------------------------------------------------------
## vehicle_type: Truck
## tested_transmission_type: Semi-Automatic
## rated_horsepower equivalent_test_weight_lbs rnd_adj_fe
## n 93.0000 93.0000 93.000000
## mean 353.1290 5190.8602 27.156989
## stdev 102.9612 668.9928 6.903471
## min 188.0000 4000.0000 12.500000
## max 700.0000 7000.0000 42.700000I calculated the confidence interval at 90%, 95%, and 99% confidence levels for the mean fuel economy of Automatic Vehicle in the data set. The results for each confidence interval are displayed below. It can be seen as the confidence level gets higher the range of where the population mean ending up in the range gets larger. The 90% confidence interval was 50<=mu<=60 comparing this to the 99% confidence interval it can be seen it gets wider moving to 47<=mu<=64. To form this confidence interval we used a t-test as the population standard deviation was unknown the sample size was greater than 30 representing a normal distribution. As the degree of freedom get larger with sample size the t-distribution more closely represents a normal distribution. In turn as the confidence interval gets larger so does the t-value creating a wider range. Of these options I would select a 95% confidence interval allowing for a combination of accuracy and confidence in our mean following within the interval.
## [1] "The 90% confidence interval for the mean adjusted fuel economy (RND_ADJ_FE) of automatic vehicles is: 50 <= mu <= 60 ."## [1] "The 95% confidence interval for the mean adjusted fuel economy (RND_ADJ_FE) of automatic vehicles is: 49 <= mu <= 62 ."## [1] "The 99% confidence interval for the mean adjusted fuel economy (RND_ADJ_FE) of automatic vehicles is: 47 <= mu <= 64 ."## [1] "The 95% confidence interval of mean adjusted fuel economy of manual vehicles is: 31 <= mu <= 41 ."## [1] "The 90% confidence interval for the mean horsepower of cars is: 337 <= mu <= 377 ."## [1] "The 95% confidence interval for the mean horsepower of cars is: 333 <= mu <= 381 ."## [1] "The 99% confidence interval for the mean horsepower of cars is: 325 <= mu <= 389 ."## [1] "The 90% confidence interval for the mean horsepower of trucks is: 300 <= mu <= 324 ."## [1] "The 95% confidence interval for the mean horsepower of trucks is: 297 <= mu <= 326 ."## [1] "The 99% confidence interval for the mean horsepower of trucks is: 293 <= mu <= 331 ."Kabacoff, R. I. (2015). R in Action (2nd ed.). Manning Publications.
Bluman, A. G. (2018). Elementary statistics: A step by step approach (10th ed.). McGraw Hill.