Yamaha G2 Trouble moving & Question about air hose

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Hi, I've had this golf cart for a pretty long time now and I use it on and off about every couple months. Recently it has been having issues moving, what I mean by this is that when I switch it to drive/reverse, it sometimes refuses to catch. Holding the choke down while in neutral will most of the time start it just fine, and it will rev nice.

I've ordered a tune up kit with the basic stuff like new belts, new filters, new spark plug etc. and I am hoping it will fix it. My question about the air hose is, where the air box end connects to the carb, should the hose be **on** the carb connector? I found it just dangling off, barely even close to being connected so I had to stretch the end out a bit to put it back on and clamp it down. Did I do that right?

I should mention that after putting it on all the way air tight, it has been starting a bit better but will now hesitate to go above half throttle. It is raining where I am so is it possible the rain is causing that?

I would post pictures but I haven't been registered for 7 days so I cannot do that