Talking about my personal experience, I can say without any doubt that the design of your website can have a great impact on your customers. I own a start-up, the website of which had all the detail of our services greatly written. But it was not getting enough customers. It was then when I started asking for feedback about my website from my friends and got to know that it was the design that needs to be improved. I changed the design to an attractive, simple and responsive one and saw an increase in the number of visitors as well as clients.
The blog i was reading: http://www.digitalaptech.com/how-web-design-impacts-customer-experience/ talks about some ways you can use to improve our web design and increase customers