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#1
07-13-2012, 03:40 PM
 NoSpoon Member SOA Join Date: Jun 2012 Location: Coruscant Studying for MLC College: Senior, UMASS Amherst Favorite beer: BBC Steel Rail Posts: 36
Help with stats problem!!!

So my stats teacher and I have a disagreement. The following was a homework question and the two relevant multiple choice answers:

If a null hypothesis was rejected at a significance level of 0.05, then:

A. We would have rejected the null hypothesis at the sig. level of 0.01 but not necessarily at sig. level of 0.1.

D. We would have rejected the null hypothesis at the sig. level of 0.1 but not necessarily at sig. level of 0.01.

I know why he picked the answer that he did, but I believe it should be the opposite. What do people think the correct answer should be and why? I'm not going to put which answer I think is correct to avoid biases.

Thanks!
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#2
07-14-2012, 07:30 PM
 Practicing Member SOA Join Date: Sep 2010 Location: NYC Posts: 569

A.

Significance level refers to the probability that the sample data was selected given that the null hypothesis is correct. When rejecting the null hypothesis at a significance level of .05, we are stating that if the probability of our specific sample data being selected is less than .05 given our null hypothesis, we will reject the null. This statement includes the level of .01 but not necessarily the level of .1.
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#3
08-18-2012, 06:53 PM
 Eric61483 Member Join Date: Nov 2009 Posts: 120

D.

P value, not level of significance, refers to the probability that the sample data was selected given that the null hypothesis is correct. The null hypothesis is rejected when P < level of significance. If null hypothesis is rejected at 0.05, then P < 0.05. It follows then that P < 0.1, so the null hypothesis is rejected at 0.1. We are not sure how P compares to 0.01, though.
#4
08-18-2012, 10:09 PM
 clarinetist Member Join Date: Aug 2011 Location: Minnesota Studying for Exam MFE College: 3rd Year Posts: 268

Let P be the given P value. If a null hypothesis is rejected at $\alpha = 0.05$, then $P < 0.05$. Since $P < 0.05$, $P < 0.1$, which means that if $\alpha = 0.1$, the null hypothesis will be rejected. However, we cannot guarantee that $P < 0.01$. The answer must therefore be D.
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#5
08-20-2012, 02:25 PM
 NoSpoon Member SOA Join Date: Jun 2012 Location: Coruscant Studying for MLC College: Senior, UMASS Amherst Favorite beer: BBC Steel Rail Posts: 36

I agree with D, but my teacher kept arguing A. I think maybe the wording is a little ambiguous...
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#6
08-21-2012, 06:41 AM
 Eric61483 Member Join Date: Nov 2009 Posts: 120

I do not see how the wording is ambiguous, assuming significance level = level of significance, which certainly would have been defined in the course.
#7
08-21-2012, 07:16 AM
 Baby, ByeBye Member CAS Join Date: Jan 2012 Location: your mom Posts: 14,158

D. Your teacher is a terd. Change schools.

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