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I'm trying to test whether or not it's true that people of similar heights tend to marry each other, and I'm a bit confused how exactly to go about it.

I have a data set with 96 pairs of the heights of husband and wife, so I thought I could just take the mean of the differences in height between husband and wife (specifically, height of the wife subtracted from height of the husband), which comes out to 10.43 cm, and then do hypothesis testing with that as my test-statistic.

This is where I'm confused, however. I thought I could have the null hypothesis be $|\mu| \geq 15$ and the alternative hypothesis $|\mu|<15$ where $\mu$ is the average difference in height between husband and wife. Calculating the $t$-value for $\hat{\mu}=10.43$ with respect to 15 yields -6.77. This is obviously less than the critical value so can I therefore reject the null hypothesis and conclude that the heights of husband and wife are, on average, similar?

Thank you.

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    $\begingroup$ Your last paragraph does not really address your original question: because women tend to be shorter than men, it seems of little value to test whether married women are shorter than married men. What might be more meaningful for your research is to test whether the taller women are married to taller men and shorter women to shorter men. $\endgroup$
    – whuber
    Jan 19, 2014 at 18:07
  • $\begingroup$ You're absolutely right. I just realized that $\mathrm{mean}(\mathrm{Husband}-\mathrm{Wife})$ is the same as $\mathrm{mean}(\mathrm{Husband}) - \mathrm{mean}(\mathrm{Wife})$. $\endgroup$
    – N4v
    Jan 19, 2014 at 19:45

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one questions : why you set your Null hypothesis like this ? (how you come up to set mean to 15).

Basically, for every statistical testing, the null hypothesis already defined. for example,in your case, you would assume the your Null hypothesis is: μ=o ,then you will calculate the T-test for it and w.r.t the P-value, either you will reject or accept your Null hypothesis.

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  • $\begingroup$ Thank you. I set mean to 15 because I figured if the mean is above 15 then men don't tend to marry women of similar heights. $\endgroup$
    – N4v
    Jan 19, 2014 at 19:59
  • $\begingroup$ so if it's helped you, like it :P $\endgroup$ Jan 19, 2014 at 20:13
  • $\begingroup$ Sorry, but I can't upvote because I don't have enough reputation. $\endgroup$
    – N4v
    Jan 19, 2014 at 23:50

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