"calculate the number of permutations possible when using the first five letters of the alphabet to create 3-letter words.
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Answer:
So the p value is higher the significance level given 0.1, so then we can conclude that we FAIL to reject the null hypothesis that the difference mean between after and before score is equal 0. So then we don't have enough evidence to say that the score for the second exam is different than the score for the first exam.
Step-by-step explanation:
Previous concepts
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 (first exam) , y = test value after (second exam)
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
The first step is calculate the difference
The statistic given by :
The next step is calculate the degrees of freedom given by:
Now we can calculate the p value, since we have a left tailed test the p value is given by:
So the p value is higher the significance level given 0.1, so then we can conclude that we FAIL to reject the null hypothesis that the difference mean between after and before score is equal 0. So then we don't have enough evidence to say that the score for the second exam is different than the score for the first exam.