$-z_\frac{\alpha}{2}$ and $z_\frac{\alpha}{2}$ in Confidence Intervals I was watching a Youtube video about Confidence Intervals and came across a slide that threw me:

I get that the blue region is $1-\alpha$ (often 0.95 in practice) while the bits to the edge are each $\frac{\alpha}{2}$ (often 0.025 in practice).
However, I don't understand the tick marks down the bottom. Why can't they instead be respectively $z_{\frac{\alpha}{2}}$ and $z_{1-\frac{\alpha}{2}}$, so that in the case of a 95% Confidence Interval they'd come out as $z_{0.025}$ and $z_{0.975}$. Those values come out to -1.96 and 1.96, as per the following R code
qnorm(0.025)
qnorm(0.975)

I must be missing something obvious because this video has many comments but nobody has previously tried to 'correct' it. It'd be much appreciated if someone could explain how the tick-marks in the video are in fact correct, and why my interpretation is wrong or not as accurate.
There is a related question, in which the poster says

I got used to the convention that $z_{\frac{\alpha}{2}}$ is such a
value that $P(Z>z_\frac{\alpha}{2}) = \frac{\alpha}{2}$. It also
follows that $-z_{\frac{\alpha}{2}} = z_{1-\frac{\alpha}{2}}$

However, I still don't understand the logic of the convention, or why it should be preferred to just writing the tick marks as $z_{\frac{\alpha}{2}}$ and $z_{1-\frac{\alpha}{2}}$.

I suspect the convention arose when people had to look up z-scores by hand in a printed table. But it's also a convention that makes the arithmetic & concepts slightly easier to work with. Nothing deeper than that.

*

*Why write in terms of $-z_{\alpha/2}$ instead of $z_{1-(\alpha/2)}$?
Since the standard Normal distribution is symmetric, it's faster to look up one value e.g. $z_{\alpha/2}$ and negate it to get the other value. As soon as you've found one value, it's a waste of time to also look up $z_{1-(\alpha/2)}$ in a table.
Also, conceptually, I find it more useful to think about a CI as "estimate plus/minus margin of error" rather than "estimate plus two arbitrary other numbers (of which one might be negative)."


*Why treat $z_{\alpha/2}$ as the upper $\alpha/2$ percentile, not the lower percentile?
In my experience, Intro Stats students seem to find it sliiiightly easier to think about "There's 2.5% in each tail, so let's look up the tail percentile that gives us a positive number" compared to thinking "...so let's look up the lower percentile, and then we'll have to negate a negative number."
