t-statistic before-after

Question

I’m doing an exercise on the Udacity's Intro to Inferential Statistics course (Problem set 10b) where I need to calculate the t-statistic on a before\after treatment situation. My null hypothesis would be that the treatment has no effect and the alternative is that the treatment will reduce the values (so I’ll be doing a one tailed test on the negative direction)

The values before are [8, 7, 6, 9, 10, 5, 7, 11, 8, 7] (mean 7.8) and the after are [5, 6, 4, 6, 5, 3, 2, 9, 4, 4] (mean 4.8)

My t-critical at alpha = 0.05 is -1.83

I thought that I could calculate it by calculating the standard error of the mean (which is the standard deviation of the differences (1.33) divide by sqr(10) -> 0.421637) And then divide the mean difference (-3) by the standard error of the mean, resultin in -7.11

But that is not the value I’m looking for.

Can someone indicate where is the problem please?

Here are the calculations:

Before  After       Difference
8         5           -3
7         6           -1
6         4           -2
9         6           -3
10        5           -5
5         3           -2
7         2           -5
11        9           -2
8         4           -4
7         4           -3


            SD ifference    1.333333333



Standard Error of the mean:         0.421637021 
Mean differences            -3  
            t   -7.115124735

Here's the link to the question (https://www.udacity.com/course/viewer#!/c-ud201/l-1905528537)

Answer 1

You did the problem correctly; the site did not. It committed a well-known error of not retaining intermediate results to sufficient precision, causing its final answer to be erroneous.

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Forensic Analysis

This site takes the student through a guided sequence of questions to go through the steps of conducting a t-test. After formulating null and alternative hypotheses, the student is asked to compute intermediate results such as the mean difference (-3) and its standard error (approximately 0.421637). However, it insists that the values be entered only to limited precision. The only way to proceed is to round the SE to 0.42. At this point, the system requires the student to replace the correct value of the SE with the rounded value. This causes the correct t-statistic, approximately equal to -7.115125, to be computed as -3/0.42 = -7.14. That (or something very close to it) is the answer one must enter in order to proceed!

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Post-Mortem Rant

The pedagogical errors in this approach are appalling: the practice of statistics is reduced to remembering names for situations and procedures, using them to look up and compute a series of formulas. Correct answers and many near-correct answers are considered wrong. Forcibly incorrect answers have to be propagated through a calculation ultimately to produce an incorrect final answer. Students are reduced to guessing what the site might accept, without having any guidance concerning the errors they might possibly have made. It is difficult to imagine a nastier climate in which to try to learn anything.