Your website is the hub of your online business; it is the virtual representation of your company whether your company exists physically or not. When you are doing business online, people cannot see you physically like how they could if they were dealing with an offline company. Hence, people do judge you by your covers. This is where a good design comes in.
Imagine if you are running an offline company. Would you allow your salespersons to be dressed in shabby or casual clothes when they are dealing with your customers? By making your staff wear professionally, you are telling your customers that you do care about quality. This works simply because first impressions matter.