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.

• 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.
– whuber
Commented Jan 19, 2014 at 18:07
• You're absolutely right. I just realized that $\mathrm{mean}(\mathrm{Husband}-\mathrm{Wife})$ is the same as $\mathrm{mean}(\mathrm{Husband}) - \mathrm{mean}(\mathrm{Wife})$.
– N4v
Commented Jan 19, 2014 at 19:45