Is mean Highway MPG significantly larger than City MPG at 99% confidence? Is it

Question

Is mean Highway MPG significantly larger than City MPG at 99% confidence? Is it larger by at least 5 gallons (using the same confidence level)? Approximate how many gallons are required to make this finding no longer significant.

Model Eng Size Cylinders MSRP City Mpg Highway Mpg Weight Type Country Range_Rover_HSE 4.4 8 $           72,285 12 16 5,379 SUV England S-Type 3 6 $           43,730 18 26 3,777 Sedan England X-Type 2.5 6 $           29,330 19 28 3,428 Sedan England XJ-Series 4.2 8 $           69,330 18 28 3,803 Sedan England Cooper 1.6 4 $           19,899 24 33 2,678 Sedan England G500 5 8 $           76,900 12 14 5,423 SUV Germany Touareg 3.2 6 $           35,900 15 20 5,086 SUV Germany S-Class 4.3 8 $           74,250 17 24 4,160 Sedan Germany A8_L 4.2 8 $           68,500 17 24 4,399 Sedan Germany A6 2.7 6 $           42,650 18 25 3,836 Sedan Germany 745i 4.4 8 $           69,300 18 26 4,376 Sedan Germany E-class 3.2 6 $           50,575 19 27 3,691 Sedan Germany 5_Series 2.5 6 $           39,800 19 28 3,428 Sedan Germany Jetta_GLI 2.8 6 $           23,210 21 29 3,179 Sedan Germany 3_Series 2.5 6 $           28,100 20 29 3,219 Sedan Germany C-class 1.8 4 $           29,250 22 30 3,250 Sedan Germany Passat_GL 1.8 4 $           22,855 21 30 3,322 Sedan Germany A4 1.8 4 $           25,550 22 31 3,252 Sedan Germany Sequoia_SR5 4.7 8 $           35,155 14 17 5,270 SUV Japan Xterra_XE 3.3 6 $           20,500 15 19 3,777 SUV Japan FX35 3.5 6 $           36,050 16 22 4,215 SUV Japan Element_EX 2.4 4 $           19,700 22 26 3,441 SUV Japan MPV_LX 3 6 $           23,490 18 25 3,772 Minivan Japan Odyssey_EX 3.5 6 $           26,990 18 25 4,365 Minivan Japan Sienna_LE 3.3 6 $           24,480 19 27 4,120 Minivan Japan GS_300 3 6 $           38,875 18 25 3,649 Sedan Japan LS_430 4.3 8 $           55,375 18 25 3,990 Sedan Japan G35 3.5 6 $           28,150 18 26 3,336 Sedan Japan TL_3.2 3.2 6 $           32,650 20 28 3,575 Sedan Japan Altima 2.5 4 $           19,200 23 29 3,088 Sedan Japan Avalon_XL 3 6 $           26,965 21 29 3,428 Sedan Japan ES_330 3.3 6 $           31,725 20 29 3,460 Sedan Japan Aerio 2.3 4 $           15,199 25 31 2,676 Sedan Japan TSX 2.4 4 $           26,490 22 31 3,318 Sedan Japan Camry_SE 2.4 4 $           20,705 23 32 3,186 Sedan Japan Accord_LX 2.4 4 $           20,100 24 33 3,164 Sedan Japan Sentra 1.8 4 $           14,400 28 36 2,581 Sedan Japan Civic_LX 1.7 4 $           16,160 29 38 2,606 Sedan Japan Corolla_LE 1.8 4 $           14,780 32 40 2,524 Sedan Japan Prius 1.5 4 $           20,295 60 51 2,890 Sedan Japan Legacy_L 2.5 4 $           21,520 22 28 3,400 Wagon Japan Matrix 1.8 4 $           15,470 27 32 2,756 Wagon Japan xB 1.5 4 $           14,480 30 34 2,469 Wagon Japan Sedona_EX 3.5 6 $           22,085 15 20 4,802 Minivan Korea Sonata 2.4 4 $           16,799 22 30 3,217 Sedan Korea Elantra 2 4 $           15,155 26 33 2,606 Sedan Korea XC90_T6 2.9 6 $           40,695 15 20 4,639 SUV Sweden 9-5_Aero 2.3 4 $           39,860 19 28 3,470 Sedan Sweden S40_TS 2.5 5 $           26,990 22 31 3,126 Sedan Sweden V40 1.9 4 $           25,700 22 29 2,822 Wagon Sweden H2_Lux 6 8 $           52,920 11 11 6,400 SUV US Navigator_Ultimate 5.4 8 $           56,140 17 12 6,041 SUV US Escalade 6 8 $           55,110 13 17 5,571 SUV US Espedition_XLT 5.4 8 $           37,475 13 17 5,671 SUV US Explorer_XLT 4.6 8 $           32,605 15 19 4,469 SUV US Mountaineer 4.6 8 $           38,335 14 19 4,523 SUV US Tahoe_SLE 4.8 8 $           37,200 15 19 5,262 SUV US Yukon_SLE 4.8 8 $           37,810 15 19 5,262 SUV US Grand_Cherokee_Freedom 4.7 8 $           33,142 15 20 4,203 SUV US Envoy_XL 4.2 6 $           33,470 15 20 4,968 SUV US Bravada 4.2 6 $           35,870 15 21 4,600 SUV US Trailblazer_LT 4.2 6 $           32,170 15 21 4,616 SUV US Ranier_CXL 4.2 6 $           38,645 15 21 4,628 SUV US Liberty_Sport 2.4 4 $           18,380 19 24 3,648 SUV US Escape_XLS 3 6 $           20,400 19 25 3,181 SUV US VUE 2.2 4 $           19,005 22 28 3,260 SUV US Astro_LS 4.3 6 $           25,230 16 20 4,309 Minivan US Freestar_SE 3.9 6 $           26,390 17 23 4,275 Minivan US Venture_Plus 3.4 6 $           21,475 19 26 3,699 Minivan US Montana_FWD 3.4 6 $           23,335 19 26 3,803 Minivan US Caravan_SE 2.4 4 $           18,330 21 27 3,908 Minivan US Viper 8.3 10 $           81,090 12 21 3,410 Sedan US Grand_Marquis_GS 4.6 8 $           25,520 17 25 3,957 Sedan US Crown_Victoria_LX 4.6 8 $           27,220 17 25 4,057 Sedan US Taurus_SES 3 6 $           21,805 19 26 3,306 Sedan US CTS 3.2 6 $           30,650 19 26 3,509 Sedan US Intrepid_SXT 3.5 6 $           25,105 19 27 3,548 Sedan US Concorde_Lxi 3.5 6 $           26,210 19 27 3,548 Sedan US PT_Cruiser 2.4 4 $           17,490 22 29 3,101 Sedan US LeSabre 3.8 6 $           25,865 20 29 3,567 Sedan US Impala_LS 3.8 6 $           24,685 20 30 3,466 Sedan US Grand_Prix_GT2 3.8 6 $           24,075 20 30 3,484 Sedan US Focus_SE 2 4 $           15,155 26 33 2,606 Sedan US Vibe 1.8 4 $           16,605 29 36 2,700 Wagon US

Explanation / Answer

Here we will say that these two data (Highway MPG and CIty MPG) are paired so we can get the paired difference data in the given table and then we will calculate its 99% confidence interval.

Mean difference dbar = 6.4524

Std. Dev. of differences sd = 2.9058  

Standard error of differences sed = sd /sqrt(n) = 2.9058/ sqrt(84) = 0.317

99% confidence interval = dbar +- tdf, 0.01 sed = 6.4524 +- t83,0.01 * 0.317

=6.4524 + 2.6364 * 0.317

= (5.6167 mpg, 7.2881 mpg)

so as the confidence interval doesn't consist value of zero and contains positive value that means highway mpg is greater than city mpg. Yes, it is larger than 5 gallons too as confidence interval is greater than 5 mpg. It requires a value of 5.62 mpg to make the difference insignificant.

Model City Mpg Highway Mpg Difference Range_Rover_HSE 12 16 4 S-Type 18 26 8 X-Type 19 28 9 XJ-Series 18 28 10 Cooper 24 33 9 G500 12 14 2 Touareg 15 20 5 S-Class 17 24 7 A8_L 17 24 7 A6 18 25 7 745i 18 26 8 E-class 19 27 8 5_Series 19 28 9 Jetta_GLI 21 29 8 3_Series 20 29 9 C-class 22 30 8 Passat_GL 21 30 9 A4 22 31 9 Sequoia_SR5 14 17 3 Xterra_XE 15 19 4 FX35 16 22 6 Element_EX 22 26 4 MPV_LX 18 25 7 Odyssey_EX 18 25 7 Sienna_LE 19 27 8 GS_300 18 25 7 LS_430 18 25 7 G35 18 26 8 TL_3.2 20 28 8 Altima 23 29 6 Avalon_XL 21 29 8 ES_330 20 29 9 Aerio 25 31 6 TSX 22 31 9 Camry_SE 23 32 9 Accord_LX 24 33 9 Sentra 28 36 8 Civic_LX 29 38 9 Corolla_LE 32 40 8 Prius 60 51 -9 Legacy_L 22 28 6 Matrix 27 32 5 xB 30 34 4 Sedona_EX 15 20 5 Sonata 22 30 8 Elantra 26 33 7 XC90_T6 15 20 5 9-5_Aero 19 28 9 S40_TS 22 31 9 V40 22 29 7 H2_Lux 11 11 0 Navigator_Ultimate 17 12 -5 Escalade 13 17 4 Espedition_XLT 13 17 4 Explorer_XLT 15 19 4 Mountaineer 14 19 5 Tahoe_SLE 15 19 4 Yukon_SLE 15 19 4 Grand_Cherokee_Freedom 15 20 5 Envoy_XL 15 20 5 Bravada 15 21 6 Trailblazer_LT 15 21 6 Ranier_CXL 15 21 6 Liberty_Sport 19 24 5 Escape_XLS 19 25 6 VUE 22 28 6 Astro_LS 16 20 4 Freestar_SE 17 23 6 Venture_Plus 19 26 7 Montana_FWD 19 26 7 Caravan_SE 21 27 6 Viper 12 21 9 Grand_Marquis_GS 17 25 8 Crown_Victoria_LX 17 25 8 Taurus_SES 19 26 7 CTS 19 26 7 Intrepid_SXT 19 27 8 Concorde_Lxi 19 27 8 PT_Cruiser 22 29 7 LeSabre 20 29 9 Impala_LS 20 30 10 Grand_Prix_GT2 20 30 10 Focus_SE 26 33 7 Vibe 29 36 7 Average 6.4524 Std. Dev. 2.9058

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