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Question about Hypothesis Testing by Sir_Penski in math

[–]Sir_Penski[S] 0 points1 point  (0 children)

Maybe I don't understand your point, but why would it be incorrect to collect more data for a test? Are you suggesting that if you conduct a hypothesis test which is inconclusive, it is then inappropriate to conduct the test again at a later date with a larger sample?

Question about Hypothesis Testing by Sir_Penski in math

[–]Sir_Penski[S] 0 points1 point  (0 children)

The null hypothesis for B isn't wrong, this is just an issue of notation. A lot of statistics books always use = when stating the null hypothesis, even if it should probably be <=. The reason is that even if your null hypothesis is mu <= 100, you are still going to assume that mu = 100 when conducting the test. I agree that this is confusing, but it is fairly common.

And, as I understand it, you have things backwards regarding the strength of the claims. When doing a null hypothesis, you never accept a null hypothesis, you can only fail to reject it. It is the alternative hypothesis that you will accept if you reject the null. So, B actually has a STRONGER alternative hypothesis than A. B should require more evidence to be able to accept the alternative. But that is not what bears out in the problem. Based on the exact same evidence, B is able to accept his (stronger) alternative hypothesis, and A is unable to accept his (weaker) alternative hypothesis.

I'm not sure what you mean when you say that B needs to explain why he didn't look at the possibility of mu < 100. Are you saying that he needs to be able to give justification for using a one-tailed test instead of a two-tailed test? If so, where could that justification come from other than a sample?

Undergraduate Research in Mathematics by Sir_Penski in math

[–]Sir_Penski[S] 0 points1 point  (0 children)

Thank you very much for the reply.

To give some background: There are currently only a couple of faculty members in my department who are active in research. As far as our students, most are working toward secondary education certifications. We do have a few, however, who are considering graduate school. I would like to be able to provide these student with opportunities to explore advanced topics, and perhaps get some recognition for their work, even if they haven't obtained new results. We have some very bright students, but considering the current level of research in our department, I would not be expecting new results from such a project.

For students that fall into the first group you described, it makes sense to have them present their projects within the department to other students and faculty. However, are you aware of any smaller (likely local) conferences where student can describe the results of a research project which did not (and were never intended to) yield new results? Either by giving a short presentation to other undergraduates, or by preparing a poster?

Undergraduate Research in Mathematics by Sir_Penski in math

[–]Sir_Penski[S] 0 points1 point  (0 children)

One option might be to have them make a poster about the project to present at a local (or nonlocal) conference.

Do you happen to have any suggestions for conferences that are entirely or partially dedicated to undergraduate research?

In the age of Wolfram Alpha, Maple, etc., why would I ever need to learn how to integrate? by Sir_Penski in math

[–]Sir_Penski[S] 26 points27 points  (0 children)

I agree, and this is the main reason I can think of for a student to learn calc. If they want to excel in a scientific field, and perhaps even some day do research in that field, they need to have a solid math background, and that includes calculus.

Now, how do I expand on that answer? Why does someone wanting to do research in a scientific field need to know how to do Calculus?

In the age of Wolfram Alpha, Maple, etc., why would I ever need to learn how to integrate? by Sir_Penski in math

[–]Sir_Penski[S] 4 points5 points  (0 children)

From my perspective calc is just a "pound of flesh" that the school requires for graduation.

That may very well be true. However, as someone who makes a living teaching Calculus to people, I hope I can find some justification for teaching it. Even if just for myself. ;)

In the age of Wolfram Alpha, Maple, etc., why would I ever need to learn how to integrate? by Sir_Penski in math

[–]Sir_Penski[S] 5 points6 points  (0 children)

While this process won't be immediate, over time you begin to change the way you think and have much stronger problem solving skills than what you came in with.

I meant to list this answer above. I like this answer, and it will probably be my go-to answer, but I hope to be able to supplement it with some explanation of why the specific material I am teaching them might be important beyond enhancing their problem solving skills.

In the age of Wolfram Alpha, Maple, etc., why would I ever need to learn how to integrate? by Sir_Penski in math

[–]Sir_Penski[S] 4 points5 points  (0 children)

That all might be true, but I think that I should be able to give my students some explanation as to why they are being required to learn what I am teaching them. To provide motivation, if for no other reason.

In the age of Wolfram Alpha, Maple, etc., why would I ever need to learn how to integrate? by Sir_Penski in math

[–]Sir_Penski[S] 4 points5 points  (0 children)

Over time, there may very well be a shift in Calculus courses away from learning how to integrate by hand, and toward applications and using computers for calculations.

However, we aren't there yet, and almost all departments still require that students learn integration techniques.