Circle or highlight the corresponding letter/number that corresponds to your solution (or is closest to your solution) and attach R code at the end of the document for full credit. For this section, use the mtcars dataset available in R (you do not need to download any packages). Assume that the distribution of engine displacement (disp) are approximately normally distributed within transmission types (am) and the samples are drawn independently. Also assume that the data represent a simple random sample. Do not assume that the variances are equal. Write the null and alternative hypothesis to determine if the mean displacement differs by transmission type (standard = s , automatic = a) in the population. Using ? = 0.05, conduct a statistical test for the hypotheses in 1. the context of the problem.

a. P-value?

b. Conclusion Calculate a 95% confidence interval for the difference in the mean displacement of cars with automatic transmissions and standard transmissions.

.

?

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> mtcars mpg cyl disp hp drat wt qsec vs am gear carb Mazda RX4 Mazda RX4 Wag 6 160.0 110 3.90 2.620 16.46 0 1 6 160.0 110 3.90 2.875 17.02 0 1 21.0 4 4 21.0 4 4 Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 6 258.0 110 3.08 3.215 19.44 1 0 8 360.0 175 3.15 3.440 17.02 6 225.0 105 2.76 3.460 20.22 8 360.0 245 3.21 3.570 15.84 Hornet 4 Drive 21.4 1. Hornet Sportabout Valiant 18.7 2 18.1 1. Duster 360 14.3 3 4 Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 4 2 Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 4 2 6 167.6 123 3.92 3.440 18.30 6 167.6 123 3.92 3.440 18.90 8 275.8 180 3.07 4.070 17.40 8 275.8 180 3.07 3.730 17.60 8 275.8 180 3.07 3.780 18.00 8 472.0 205 2.93 5.250 17.98 0 0 8 460.0 215 3.00 5.424 17.82 0 0 8 440.0 230 3.23 5.345 17.42 0 0 Merc 280 19.2 4 4 Merc 280C Merc 450SE 17.8 4 4 16.4 Merc 450SL 17.3 3 Merc 450SLC 15.2 Cadillac Fleetwood 10.4 4 Lincoln Continental 10.4 4 Chrysler Imperial Fiat 128 14.7 4 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1. Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2 Toyota Corolla Toyota Corona Dodge Challenger AMC Javelin 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1 21.5 4 120.1 97 3.70 2.465 20.01 1 1 8 318.0 150 2.76 3.520 16.87 8 304.0 150 3.15 3.435 17.30 8 350.0 245 3.73 3.840 15.41 8 400.0 175 3.08 3.845 17.05 15.5 2 15.2 2 Camaro Z28 13.3 4 Pontiac Firebird 19.2 2 Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1. 4 1. Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 1. 2. Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1. 2 8 351.0 264 4.22 3.170 14.50 6 145.0 175 3.62 2.770 15.50 8 301.0 335 3.54 3.570 14.60 Ford Pantera L 15.8 1. 4 Ferrari Dino 19.7 1. Maserati Bora 15.0 1 8 Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2 > mtcars mpg cyl disp hp drat wt qsec vs am gear carb Mazda RX4 Mazda RX4 Wag 6 160.0 110 3.90 2.620 16.46 0 1 6 160.0 110 3.90 2.875 17.02 0 1 21.0 4 4 21.0 4 4 Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 6 258.0 110 3.08 3.215 19.44 1 0 8 360.0 175 3.15 3.440 17.02 6 225.0 105 2.76 3.460 20.22 8 360.0 245 3.21 3.570 15.84 Hornet 4 Drive 21.4 1. Hornet Sportabout Valiant 18.7 2 18.1 1. Duster 360 14.3 3 4 Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 4 2 Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 4 2 6 167.6 123 3.92 3.440 18.30 6 167.6 123 3.92 3.440 18.90 8 275.8 180 3.07 4.070 17.40 8 275.8 180 3.07 3.730 17.60 8 275.8 180 3.07 3.780 18.00 8 472.0 205 2.93 5.250 17.98 0 0 8 460.0 215 3.00 5.424 17.82 0 0 8 440.0 230 3.23 5.345 17.42 0 0 Merc 280 19.2 4 4 Merc 280C Merc 450SE 17.8 4 4 16.4 Merc 450SL 17.3 3 Merc 450SLC 15.2 Cadillac Fleetwood 10.4 4 Lincoln Continental 10.4 4 Chrysler Imperial Fiat 128 14.7 4 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1. Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2 Toyota Corolla Toyota Corona Dodge Challenger AMC Javelin 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1 21.5 4 120.1 97 3.70 2.465 20.01 1 1 8 318.0 150 2.76 3.520 16.87 8 304.0 150 3.15 3.435 17.30 8 350.0 245 3.73 3.840 15.41 8 400.0 175 3.08 3.845 17.05 15.5 2 15.2 2 Camaro Z28 13.3 4 Pontiac Firebird 19.2 2 Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1. 4 1. Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 1. 2. Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1. 2 8 351.0 264 4.22 3.170 14.50 6 145.0 175 3.62 2.770 15.50 8 301.0 335 3.54 3.570 14.60 Ford Pantera L 15.8 1. 4 Ferrari Dino 19.7 1. Maserati Bora 15.0 1 8 Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2

Answer rating: 100% (QA)

R codes and output dmtcars attachd The following objects are masked from d pos 3 ... View the full answer