Using the mtcars Dataset

Conducting a significance test can allow us to understand if changes between results or data are actually worth noting or significant or if they are present due to chance.

• Data can vary so not every change is meant to be significant
• Significance testing is meant to be used to see actual statistical differences
• In this presentation, we will test if manual or automatic have better fuel efficiency using the mtcars dataset

Our hypothesis tests whether manual cars have higher mean miles per gallon (mpg) than automatic car

\[ H_0: \mu_{manual} = \mu_{automatic} \\ H_a: \mu_{manual} \neq \mu_{automatic} \]

We will use a two-sample t-test at a significance level of \(= 0.05\), meaning if it is less than the level, the decision will be rejected.

# Perform the 2 sample t-test and display the results
t_test_result <- t.test(mpg ~ am, data = mtcars)
print(t_test_result)

## 
##  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 between group Automatic and group Manual is not equal to 0
## 95 percent confidence interval:
##  -11.280194  -3.209684
## sample estimates:
## mean in group Automatic    mean in group Manual 
##                17.14737                24.39231

As decided earlier, if the p-value < 0.05, we reject the null hypothesis.

Otherwise, we fail to reject it.

From our test:

• p-value = 0.0014
• Mean (Manual) = 24.39
• Mean (Automatic) = 17.15

\[ \text{Decision: Reject } H_0 \text{ if } p < 0.05 \]

• From the t-test we saw that manual transmission has a higher MPG average then automatic cars
• We can say that the difference is statistically significant.
• Significance Testing has helped us confirm that results are not due to random variations

Application where Significance Testing is Used:

• Trauma Response Data
• Marketing
• Medical Data
• National Security