We are dealing with proportions so the proportion of 20s saying yes is 24/80=0.3, while that for 30s is 24/120=0.2. So the difference is 0.1. It's this difference we need to examine more closely later. We also need to note the sample sizes.
Let p20=0.3 and p30=0.2 and let μ=p20-p30=0.1. Statistically we can equate the proportions to the two means in a probability distribution. We can determine the variance because we have a binary situation-yes and no are the only two states. So for the individual groups:
μ20=p20=0.3 and μ30=p30=0.2, variance σ202=p20(1-p20)/n20=0.21/80=0.002625; variance σ302=p30(1-p30)/n30=0.16/120=0.001333. (We can deduce the standard deviations from these if we need them.)
What we called μ (p20-p30) is the mean for the probability distribution for the difference in proportions. The variance is simply the sum of the individual variances:
σ2=σ202+σ302=0.002625+0.001333=0.003958, so standard deviation σ=√0.003958=0.06292 approx.
The sample sizes n20=80 and n30=120 are reasonably large (bigger than 30) so we can assume a normal distribution.
A 95% confidence interval corresponds to a Z-score of 1.96, a two-tailed value because we are considering a data range [low,high] on either side of the mean, so the 100-95=5% is distributed equally between the left and right tails of the distribution. We are actually looking at the Z-score corresponding to 100-5/2=97.5%=0.975 (Z=1.96) when we inspect the body of the distribution table. Z=(X-μ)/σ for some value X in the dataset. We are looking for a low X value and a high X value to give us a 95% confidence interval. So:
|X-μ|/σ=1.96, from which X=μ±1.96σ=0.1±1.96×0.06292. The confidence interval is about [-0.02,0.22]. We can be 95% confident that the proportion difference lies between these two extremes. This means that in a population -0.02≤p20-p30≤0.22. (This appears to allow for a small minority of 20-29 year olds to actually be a little less impacted than 30-39 year olds; but the majority of 20-29 year olds will be impacted at least as much as 30-39 year olds.)