You have been asked to assess the effectiveness of a new teaching tool. A sample of 25 students from your classes have been tested before and after the provision of the tool, so each student has two measurements associated with them. You are testing: (a) Has the teaching tool changed student performance? (b) Is there more variability in the tool's effect than you want?

For the purpose of this assessment you can assume that your data is as normally distributed as you need it to be. The third column in this dataset corresponds to the variance value necessary for part (b). For each of these tests provide the following: What are H, and HA? (I) (ii) What is the test statistic, and under the null hypothesis what is its sampling distribution? (iii) Determine the region of rejection for a = 0.05. (iv) Is your test statistic in the region of rejection? Write a sentence or two about the determination. (v) Using Excel, R, or otherwise calculate the p-value. (vi) What can you conclude about your hypotheses from the p-value with respect to a = 0.05? (vii) Build a 95% CI that corresponds to the hypotheses. Finally (c) Produce a histogram of the sample differences that you used for part (a).[![enter image description here][1]][1]

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I did a paired t-test for question a) where the null hypothesis was rejected, which concluded that the teaching tool improves performances. However, I am stuck as to what needs to be done for question b) and how it needs to be approachd?

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    $\begingroup$ Please type your question as text, do not just post a photograph or screenshot (see here). When you retype the question, add the self-study tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. $\endgroup$ Commented May 23, 2022 at 11:48
  • $\begingroup$ How is variance computed for each student and (especially) why are all of the "variances" exactly $3.8?$ $\endgroup$
    – BruceET
    Commented May 23, 2022 at 21:43

1 Answer 1


Clearly, this is a trick question. It would be inappropriate to assess performance before and after using the teaching tool to conclude something about the effectiveness of the teaching tool. You would have to consider what would have happened without the teaching tool under some suitable alternative scenario (e.g. something unrealistic like no further teaching of the subject, or perhaps the traditional or current way the subject is taught, or whatever else makes sense in the context). Ideally, you'd want a randomized experiment of one approach vs. the other, but at least (=much more likely to have bias issues) a comparison vs. what we believe we know about alternative approaches.

  • $\begingroup$ You have the correct take on this. But, these questions are often asked asked in a cause and effect manner in university settings without regard to the point you are bringing up. $\endgroup$ Commented May 23, 2022 at 15:53

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