Answer:
t48 = 1.7500
Step-by-step explanation:
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value before , y = test value after
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
We have the mean difference
And the sample standard deviation for the differences, is:
Now we can calculate the statistic given by :
Since we don't have the population standard deviaition we need to use the t distribution and we can calculate the degrees of freedom given by:
Now we can calculate the p value, since we have a right tailed test the p value is given by:
If we use a significance level of 5% we have that , and on this case we reject the null hypothesis
. And we don't have enough evidence to conclude that the difference of means it's higher than 50 points.