If you have shared hosting I would first optimize the site from plugins, caching, optimizing image sizes, and as far as condensing php and css files.

Next step would be CDNs/Cloud services.

Can you give more details on the site itself? Just because a site takes long to load, doesn't necessarily mean you need to upgrade - it could possibly be the host. We need more details..

Dedicated wordpress hosting can give you speeds up to 4 x faster

This all depends upon your Website and what you decide the "next step up" actually is. Is it a semi-dedicated, VPS, or dedicated server? Also, why is your site running slowly right now? Is it really due to your hosting account or are you running slow plugins, for example? There are many considerations that must be addressed before answering your question. However, one thing is true: 28 seconds is way too long of a load time!

Are you absolutely sure the 28 second load time is (on average) the case with every visitor and not just your connection slowing down, maybe?

Beyond that, there's a lot of factors you could take into account before you go for an upgrade. You might not need an upgrade, just an optimization, possibly.