Very simple chi-square question I have a super simple  chi-square in R question, but I'm struggling to wrap my head around it. The question was to take a random 20 people from the dataset, count males and females and then use chi-square test to accept/reject the null hypothesis that half of the population in the entire large dataset is men.
So this is my data table:

How can I run chisq.test on just 2 numbers? Or should there be an 'expected' column with values of 10 for each row and then run the function? I haven't been able to find a similar chi-square problem on the internet.

You are using the wrong test.  While you could run chi squared test (with expected values of 10 and 10) and 1 degree of freedom, there is a much better way.  You haven't found examples like this because you should use a binomial test instead.
Given the null hypothesis (and quite reasonable assumptions on the large size of the population and the sampling method) the number of females would have a binomial distribution  B(20,0.5).
So you use the binomial distribution to find a (say) 95% acceptance region.  The exact region depends on if you want a two-tail or one-tail test. But 6≤n≤14 works for me.
And then reject your null hypothesis if the observed value of female lies outside that region.
