# Frequency Distribution Test Vs. Chi Square Goodness of FIt

I need to prove that the higher frequency of an occurrence within a particular range is statistically significant. Let me explain this with an example:

X-axis has ages and Y-axis has the frequencies of humans sleeping more than 10 hours a day.
I need to prove that people below 10 years and above 80 years of age sleep more than 10 hours a day compared to those in other age groups (such as 10-20 yrs, 20-30,.... 50-60, etc.). A simple histogram can show you higher frequency but then each group also has different universe size. So something like hitrate might not be statistically correct.

I have looked into Chi-Square Goodness of Fit test but I'm not sure what a good choice of expected frequency would be in this case. Can you suggest the right approach to do this? Thanks.

First, you can't prove this with statistics, you can just offer evidence.

That said, I would look into regression models. Given that you want to show something about specific ages, you could use a model like this:

$Y = b_0 + b_1\mathrm{age} + b2(\mathrm{age}<10) + b3(\mathrm{age}> 80)$

But that would not say anything about 10 hours, specifically. If you want to look at that exact number then you could do a crosstab table of "slept over 10 hours" (yes/no) vs. "between 10 and 80 years old" (yes/no) and then do a chi-square test.