# Thread: Doesn't "At least" mean greater than

1. ## Doesn't "At least" mean greater than

Thank you for taking the time to read my question

I was given a question that reads: We would like to test whether the percentage of students who have student loan is AT LEAST 25%. 120 students have the loan. There is a total of 500 students.

To me, H1 should be upper tail test since you are testing for those who have
at least 25% which to me is more than 25 %.

So I would write Ho: π . ≤25
H1: π >.25

But I am wrong. The professor's answer key says it is a lower tail test. Could someone please explain to me how this is possible and where my thinking is wrong. I believe that H1 is what you are testing and therefore should be greater than.

2. ## Re: Doesn't "At least" mean greater than

Originally Posted by ealeql
at least 25% which to me is more than 25 %.
Nah. . .
http://en.wiktionary.org/wiki/at_least

3. ## Re: Doesn't "At least" mean greater than

So "at least 25" really means 1-24. Thank you very much for taking the time to answer that. Do you happen to know where a list is online with the translation of mathematical expressions such as "at least" "more than"? I think I should review these before my test.
Thanks again

4. ## Correction: Perhaps this is not correct.

I just checked in my elementary stats notes and it states that when X = at least 120 that means 120, 121, 122 ....

5. ## Re: Doesn't "At least" mean greater than

I just checked in my elementary stats notes and it states that when X = at least 120 that means 120, 121, 122 ....
Yep. "At least" = greater than or equal to.

6. ## Re: Doesn't "At least" mean greater than

Thanks for confirming this. So how would you write the Null Hypothesis and Alternative.Kindly explain your reasoning.
Thank you very much.

7. ## Re: Doesn't "At least" mean greater than

There is nothing explicit in the question that gives direction as to which way round one would want to word the null and alternative hypotheses. This may explain why your professor is talking about a lower tail test while you're thinking of the upper tail.

Instinctively, I would frame the null and alternative hypotheses:

H0: p < .25
H1: p >= .25

A significant p value for the test would then mean that one could reject a null hypothesis of the proportion being less than 0.25 in favour of the alternate hypothesis (.25 or greater). But perhaps your prof wants you to see if there is evidence to reject the hypothesis of p >= 0.25.

8. ## Re: Doesn't "At least" mean greater than

Thank you for confirming the question is confusing and Ho and H1 could be written either way, depending on the reader's interpretation!! My thinking
was similar to yours.

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