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In the following statement, what would be the null and alternative hypothesis? The researcher wants to test (at the 1% level), whether the true mean score is at least 5 points.

I got confused because I have learned that Ha is not supposed to have the equal sign so even if it says at least, is it okay to write this hypothesis?:

$$ H_0: \mu = 5 \\ H_a: \mu > 5 $$

Taylor
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  • yes, that looks good – Taylor Jul 22 '18 at 18:15
  • The formal hypothesis should be in line with the research question, so it looks wrong. I'd prefer a correctly specified version and add a comment like "Note that - under some continuity assumptions - this is equivalent to...". – Michael M Jul 22 '18 at 18:26
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    Why not : Ho: u < 5 and Ha: u >= 5? In your current setup, what happens if u = 3? Also, you require “at least 5 points” difference which should be reflected in your hypothesis. – Todd D Jul 22 '18 at 18:59
  • Is this a homework problem from a textbook? If so please add the self-study tag. Also, I recommend a different textbook. Here is why. You can't form a proper null hypothesis in this case. If the research hypothesis was that the true mean score is greater than 5, we'd be okay. As stated we do not have a null value to use in our statistical model. We are often testing whether we can reject the null that the population parameter is exactly zero. However, we can use another value, such as exactly 5. What value would we use in this case? That is, how would you construct the t- or z-test? – dbwilson Jul 22 '18 at 19:34
  • This question and these comments have the potential to be extremely confusing to beginners. I suspect the comments might reflect three or four different interpretations of the question, as well as some basic misunderstandings of statistical hypotheses. We have [thousands of threads about hypothesis testing](https://stats.stackexchange.com/search?tab=votes&q=null%20alter*%20hypothesis). – whuber Nov 19 '18 at 16:57

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