HW 8 #3

[Morgan McBurney]

When calculating the test statistic in number 3, is the mean the average of the differences of the samples or the mean of both samples added together then averaged?

[Taeho Kim]

Morgan McBurney wrote

When calculating the test statistic in number 3, is the mean the average of the differences of the samples or the mean of both samples added together then averaged?

Following the idea of paired sample design,
everything is based on the difference between the pairs.

In that sense, the average (sample mean) of the differences of the pairs 
would be the one we are looking for.

Similarly, the value S_D was also calculated based on the differences.
The standard deviation of the differences of the pairs.
But the values is already given there 0.68.

[Morgan McBurney]

Thank You! I have one more question for part 4 of problem 3, how do you set up the "pt" command? I cannot find this in my notes.

[Taeho Kim]

Morgan McBurney wrote

Thank You! I have one more question for part 4 of problem 3, how do you set up the "pt" command? I cannot find this in my notes.

No problem, Morgan.
Now, here we have two-sided test.
So the form of your p-value becomes: 2Pr[T<-|t*|]
where T follows from a t-distribution with degrees of freedom n-1.

Therefore, we use the following ''pt'' command: 2*pt(-|t*|,n-1)
That is, we still need to calculate -|t*| and use it as a first argument.
Then, n-1 is nothing but the number of differences (or pairs) -1 and use it as a second argument.