Question

In order to determine whether or not a driver’s education course improves the scores on a driving test, a sample of 6 students were given the test before and after taking the course. The results are shown below.

Let d = Score after – Score before.

Student                        Before the Course                  After the Course

1                                              83                                            87

2                                              89                                            88

3                                              93                                            91

4                                              77                                            77

5                                              86                                            93

6                                              79                                            83

Use α = 0.1 and test to see if taking the course actually increased scores on the driving test.

Reject or do not reject Ho?

Answer 1

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: taking the course actually does not increased scores on the driving test.

Alternative hypothesis: Ha: taking the course actually increased scores on the driving test.

H0: µd = 0 versus Ha: µd > 0

This is a right tailed test.

We take difference as after minus before.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

µd = 0

Dbar = 2

Sd = 3.5214

n = 6

df = n – 1 = 5

α = 0.01

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (2 - 0)/[ 3.5214/sqrt(6)]

t = 1.3912

The p-value by using t-table is given as below:

P-value = 0.1114

P-value > α = 0.01

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that taking the course actually increased scores on the driving test.