# Practice 11 Conducting Two-sample t-test in R

## 11.1 Directions

In this practice exercise, you will conduct a two-sample t-test in R.

## 11.2 A closer look at the code

Will be using the `mtcars`

data set to test the hypothesis the average miles per gallon for cars with automatic transmistions is different from cars with manual transmissions. Thus, the null hypothesis is that \(\bar{mpg}_{auto} = \bar{mpg}_{manual}\) the alternative hypothsis is that \(\bar{mpg}_{auto} \ne \bar{mpg}_{manual}\). Note that in are, `!`

is the not apoerator, so `!=`

means not equal.

### 11.2.1 Conduct the t-test

To conduct a t-test, we need the following steps

- Plot the data
- Use
`t.test()`

to conduct a two-sample t-test

#### 11.2.1.1 Step 1: Plot the Data

Use the `boxplot()`

command to plot mpg by `am`

. See Practice 06: Box plots in R. Note that `am`

is equal to 0 for automatic transmission and 1 for manual transmission.

```
# Load the data
data("mtcars")
attach(mtcars)
```

```
## The following objects are masked from mtcars (pos = 3):
##
## am, carb, cyl, disp, drat, gear, hp, mpg, qsec, vs, wt
```

```
## The following object is masked from package:ggplot2:
##
## mpg
```

```
# Plot the data
boxplot(mpg~am)
```

Note that the inter-quartile range for `mpg`

of cars is larger for manual transmissions `am=1`

than for automatic transmission `am=0`

.

#### 11.2.1.2 Step 2: Use `t.test()`

to conduct the test.

```
# conduct t-test
t.test(mpg~am, mu=0, conf.level = 0.95, alternative = "two.sided")
```

```
##
## Welch Two Sample t-test
##
## data: mpg by am
## 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:
## -11.280194 -3.209684
## sample estimates:
## mean in group 0 mean in group 1
## 17.14737 24.39231
```

## 11.3 R code used in the VoiceThread

```
# Load the data
data("mtcars")
attach(mtcars)
# Plot the data
boxplot(mpg~am)
# conduct t-test
t.test(mpg~am, mu=0, conf.level = 0.95, alternative = "two.sided", var.equal=F)
```

## 11.4 Now you try

Use R to complete the following activities (this is just for practice you do not need to turn anything in).

Using the `mtcars`

data set, test the is average miles per gallon is the same for transmission type.