Question

You want to test if children will exhibit a higher number of aggressive acts after watching a violent television show. The number of aggressive acts for the same 19 participants before and after watching the show are as follows:

BEFORE AFTER

4 5

6 6

3 4

2 4

4 7

1 3

0 2

0 1

4 5

1 3

2 2

0 4

2 4

5 3

3 6

3 2

1 3

0 2

5 1

Paired Sample T-test

t df p

Before after -2.559 18 0.010

Note: For all tests, the alternative hypothesis specifies that the measurement one is less than measurement two.

Note: Student's t-test

PRE/POST MEANS

Before 2.42

After 3.53

Note a= .05

Answer 1

Based on the given data:

Let denote the number of aggressive acts for the same 19 participants before and after watching the violent TV show respectively. Let denote the difference in the number of aggressive acts for the same 19 participants before and after watching the violent TV show.

To test:   Vs    (before measure < after measure implying increase in the number of aggressive acts after watching the violent TV show)   where   denote the mean difference of the paired observations.

The appropriate statistical tool to test the above hypothesis would be a Paired sample t test, the test statistic given by,

where,

= -1.11

And

= 1.883

And

Substituting the values,

Comparing the test statistic obtained with the critical value of t for alpha = 0.05 and for n - 1 = 19 - 1 = 18 degrees of freedom, from t table, t0.05,18 = 1.734

Since, t = -2.559 < 1.734 lies in the critical region, we may reject H0 at 5% level. We may conclude that children will exhibit a higher number of aggressive acts after watching a violent television show.

Also, the p-value as determined from t table lies between 0.005 and 0.01, it is less than 0.05. We find that the test result is significant. We arrive at the same conclusion as above.