Answer:
There is no significant difference between the averages.
Step-by-step explanation:
Let's call
the mean of the “sentences” group
the standard deviation of the “sentences” group
the mean of the “intentional” group
the standard deviation of the “intentional” group
Then, we can calculate by using the computer
The <em>standard error of the difference (of the means)</em> for a sample of size 8 is calculated with the formula
So, the standard error of the difference is
<em>In order to see if there is a significant difference in the averages of the two groups, we compute the interval of confidence of 95% for the difference of the means corresponding to a level of significance of 0.05 (5%). </em>
<em>If this interval contains the zero, we can say there is no significant difference. </em>
<em>Since the sample size is small, we had better use the Student's t-distribution with 7 degrees of freedom (sample size-1), which is an approximation to the normal distribution N(0;1) for small samples. </em>
We get the which is a value of t such that the area under the Student's t distribution outside the interval
is less than 0.05.
That value can be obtained either by using a table or the computer and is found to be
Now we can compute our confidence interval
and the confidence interval is
[-6.057, 0.307]
Since the interval does contain the zero, we can say there is no significant difference in these samples.