Is this the correct memory upgrade for my iMac?

I see.

Is there are reason you stayed at 10.11? We found 10.13, a free upgrade, supported all our older apps. A Late 2015 will support the newest version of mac OS, but 10.13 will give you improved browser compatibility without losing any old apps that I know of.

See: How to get old versions of macOS - Apple Support for the official download link for High Sierra 10.13.

Without data I can ask three pertinent questions:

Is the computer slow to boot?

Are apps slow to launch?

Once launched, do those apps sewm to run OK?

Three "Yes" answers suggest the mech hard drive issues we discussed.

Do you have a mech-only drive, or a Fusion (hybrid) drive? Check "About this Mac..." > Storage tab or Disk Utility for drive type.

I have a late 2015 iMac which is now running pretty slow and I need to speed things up.

Based on long history here, there is a 95+% chance that adding RAM will change nothing in your current situation. Nearly all slow iMac complaints here turn out to be slow mechanical drives, not too-little RAM. Newer macOS versions appear optimized for fast solid-state drives (SSDs) The fastest roto hard drive transfer data and between 150 and 180MB/sec. The SLOWEST SSD option available to you will do 400MB/sc.

Before you nip off to spend money, let's make decisions based on data. We can see hard performance data for your current drive and RAM without compromising your security or privacy performance if you post a EtreCheck report. We can quickly and within the limited confines of these forums help you determine what issues are at play if you use EtreCheck Pro, available here:

https://etrecheck.com/index

The free version will do nicely for this purpose, although the app is worthy of our financial support.

Etrecheck is the development of a long-serving and trusted contributor here expressly for displaying information in these forums to help us help you. It will not reveal any personal or secure information.

Run it, select “Report" from the left-hand pane (scroll down to the bottom of that pane to find):

When its report displays, click the "Share Report" icon from EtreCheck’s toolbar and then "Copy report” from the resulting dropdown.

⚠️ Please DO NOT highlight the text in the report before using Etrecheck’s “Copy report” command—that will garble the formatting and make the report slower and harder to evaluate.

NOTE: Changes in late 2018 to the forum software require you use the “Additional Text" icon (see example below) to embed the report into a post:

Paste the report into the resulting “Additional Text” window:

BTW ,Crucial is the consumer outlet for Micron RAM. We have several Macs whose factor RAM was Micron.

Like Viling, I only trust Crucial or OWC.

You are welcome, and Allan Jones comments are also worth pursuing if your operating system is recent enough to run EtreCheck.

It took Apple 2 days to deliver my refurbished 2020 27-in Core I7 iMac and I had 2x16 OWC RAM modules waiting for it when it arrived.

As mentioned, just increasing the RAM is not going to speed things up for you. There are other things that are making it slow as well.

So, you really should shut it down every few days; the boot up process gets rid of a lot of unnecessary stuff.

Delete your browser history, cache, etc regularly.

Take a look at your System Preferences > User & Groups and delete everything in your login items.

If you installed any third party cleanup or AV software, uninstall it.

When you are done using an app, quit it (Command + Q) to make available those resources to other programs. Just closing the window still allows it to run in the background

If you have Google Chrome, try a different browser - it is a huge resource hog and will slow down other programs.

I purchase all of my iMac RAM from OWC and have never regretted it. LIfetime RAM warrany. This page will set you straight on compatible RAM for your iMac model.

"dozens" ?????? Quit Chrome (Command + Q) and test to see if things are better.

great to hear!