Do less bars mean a shorter battery charge?

I'm new to this forum and would like to ask everyone if they've had a similar experience with their battery life.

I have a Samsung M300 phone, bought it about 3 years ago. It's not my primary phone (I still have a landline), and my Sprint plan is very old (but it works for my budget). I am never able to get more than 2 bars in my apartment, and even on a fully charged battery I can never talk more than about 90 minutes before the battery dies. Sprint told me that there is something wrong with the battery (even though it's been doing this since I bought it). Others have said it's the phone (probably not, since my old one had the same problem).

A guy who works in a little mom and pop cell phone store told me that because I don't get a 4-bar signal in my home, the battery has to work harder to maintain a signal, and therefore will die earlier. It sort of like running the air conditioner in your car while driving - you will burn more gas faster. His explanation makes sense to me, but I'm wondering if this is correct. It's frustrating and annoying to be in the middle of a conversation (on a fully charged battery) and here the warning beeps after only 80 or 90 minutes. Of course, I can plug in the charger and continue to talk, but I can't go into another room while plugged in.

Thanks for your help.

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Don't really know if that is the correct technical explanation, but the battery does die faster where signal is lower. Happens every time I go to my uncle's house on the country