Basic questions, I know.. any help is appreciated!

I conducted a survey on people with an impairment. This survey was either filled online, or by phone: the respondent could choose.
I want to know if *the people I reached by phone are significantly more likely to be severely impaired*. Let's say my data looks like this:

------------------------------ Internet ----- Phone

Severe impairment ------- 52 ---------- 26

Not severe impairment -- 401 --------- 95

*(Not my real figures, these are slightly different)*

**Should I conduct a z-test or a chi-square test?** I would say chi-square, but I don't know how to interpret the result I get in R. *chisq.test(table(impairment, phone))*, where both phone and impairment are two binary variables, gives me: *X-squared = 1.7012, df = 1, p-value = 0.1921* **How to interpret these results?** I don't even know how to phrase my null hypothesis in a "statistical" way (both groups are just as likely to be severely impaired - **isn't there a better way to phrase this?**)

Additionally, I want to know if *the people I reached by phone are significantly more likely to be older*.

------------------------------ Internet ----- Phone

Average age ---------------- 63 ---------- 68

Since I am comparing means, I am thinking that a t-test would be appropriate, with *t.test(age ~ phone)*. My null hypothesis is that there is no difference in age among the two groups. My command in R gives me: *t = 3.3718, df = 522, p-value = 0.0008022.
Alternative hypothesis: true difference in mean is not equal to 0* . **This means that I need to reject my null-hypothesis, right?**

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