Question 1.1

What is the mean and standard deviation of mpg of the mtcars data?

mean(mtcars$mpg)
[1] 20.09062
sd(mtcars$mpg)
[1] 6.026948

Answer: The mean of mpg of mtcars is 20.09062 and the standard deviation is 6.026948.

Question 1.2

Is there sufficient evidence that the population mean score of the mtcars data exceeds 19 miles per gallon?
Answer: Yes

Question 1.3

Refer to Question 1.2, state your null and alternative hypotheses?

Answer: H_a: The population mean score of the mtcars data exceeds 19 miles per galloon or mu> 19 miles per galloon
H_0: The population mean score of the mtcars data does not exceed 19 miles per galloon or mu <= 19 miles per galloon

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 
 20.09062

Question 1.4

Is there sufficient evidence that mean difference of miles per gallon between automatic and manual cars differ statistically?
Answer: Yes

Question 1.5

Refer to Question 1.4, state your null and alternative hypotheses?
Answer: H_a: The mean difference of miles per gallon between automatic and manual cars differ statistically
H_0: The mean difference of miles per gallon between automatic and manual cars does not differ statistically

aggregate(mtcars$mpg, list(mtcars$am), mean)
  Group.1        x
1       0 17.14737
2       1 24.39231
hey<-data.frame(mtcars$am, mtcars$mpg)
library(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, union
manual<-hey %>%
  filter(mtcars.am != 0)

library(dplyr)
auto<-hey %>%
  filter(mtcars.am != 1)
t.test(manual$mtcars.mpg,auto$mtcars.mpg)

    Welch Two Sample t-test

data:  manual$mtcars.mpg and auto$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  17.14737