mtcars## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
## Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
## Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
## Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
## Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
## Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
## Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
## Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
## Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
## Fiat 128 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 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
## Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
## AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
## Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
## Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
## Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
## Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2#QUESTIONS Using the mtcars data, answer the following:
1.1 What is the mean and standard deviation of mpg of the mtcars data?
1.2 Is there sufficient evidence that the population mean score of the mtcars data exceeds 19 miles per gallon?
1.3 Refer to Question 1.2, state your null and alternative hypotheses?
1.4 Is there sufficient evidence that mean difference of miles per gallon between automatic and manual cars differ statistically?
1.5 Refer to Question 1.4, state your null and alternative hypotheses?
#ANSWERS
1.1 What is the mean and standard deviation of mpg of the mtcars data?
mean(mtcars$mpg)## [1] 20.09062sd(mtcars$mpg)## [1] 6.0269481.2 Is there sufficient evidence that the population mean score of the mtcars data exceeds 19 miles per gallon?
t.test(mtcars$mpg, mu = 19, alternative = "greater")##
## One Sample t-test
##
## data: mtcars$mpg
## t = 1.0237, df = 31, p-value = 0.157
## alternative hypothesis: true mean is greater than 19
## 95 percent confidence interval:
## 18.28418 Inf
## sample estimates:
## mean of x
## 20.09062Since the p-value > 0.05, We fail to reject the null hypothesis. Hence, there is not enough evidence to suggest that the population mean score of the mtcars data exceeds 19 miles per gallon.
1.3 Refer to Question 1.2, state your null and alternative hypotheses?
Ho: μ = 19 mpg
Ha: μ > 19 mpg
1.4 Is there sufficient evidence that mean difference of miles per gallon between automatic and manual cars differ statistically?
cars <- data.frame(mtcars$am, mtcars$mpg)
cars## mtcars.am mtcars.mpg
## 1 1 21.0
## 2 1 21.0
## 3 1 22.8
## 4 0 21.4
## 5 0 18.7
## 6 0 18.1
## 7 0 14.3
## 8 0 24.4
## 9 0 22.8
## 10 0 19.2
## 11 0 17.8
## 12 0 16.4
## 13 0 17.3
## 14 0 15.2
## 15 0 10.4
## 16 0 10.4
## 17 0 14.7
## 18 1 32.4
## 19 1 30.4
## 20 1 33.9
## 21 0 21.5
## 22 0 15.5
## 23 0 15.2
## 24 0 13.3
## 25 0 19.2
## 26 1 27.3
## 27 1 26.0
## 28 1 30.4
## 29 1 15.8
## 30 1 19.7
## 31 1 15.0
## 32 1 21.4library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionman<-cars %>%
filter(mtcars.am != 0)
man## mtcars.am mtcars.mpg
## 1 1 21.0
## 2 1 21.0
## 3 1 22.8
## 4 1 32.4
## 5 1 30.4
## 6 1 33.9
## 7 1 27.3
## 8 1 26.0
## 9 1 30.4
## 10 1 15.8
## 11 1 19.7
## 12 1 15.0
## 13 1 21.4library(dplyr)
auto<-cars %>%
filter(mtcars.am != 1)
auto## mtcars.am mtcars.mpg
## 1 0 21.4
## 2 0 18.7
## 3 0 18.1
## 4 0 14.3
## 5 0 24.4
## 6 0 22.8
## 7 0 19.2
## 8 0 17.8
## 9 0 16.4
## 10 0 17.3
## 11 0 15.2
## 12 0 10.4
## 13 0 10.4
## 14 0 14.7
## 15 0 21.5
## 16 0 15.5
## 17 0 15.2
## 18 0 13.3
## 19 0 19.2t.test(man$mtcars.mpg, auto$mtcars.mpg)##
## Welch Two Sample t-test
##
## data: man$mtcars.mpg and auto$mtcars.mpg
## t = 3.7671, df = 18.332, p-value = 0.001374
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 3.209684 11.280194
## sample estimates:
## mean of x mean of y
## 24.39231 17.14737No. as we see that the p-value is less than 0.05, hence, there’s no mean difference that is statistically significant.
1.5 Refer to Question 1.4, state your null and alternative hypotheses?
Ho: mean of the automatic cars is equal to the mean of manual cars.
Ha: mean of the automatic cars is not equal to the mean of manual cars.