The challenge is that all budgets are locked down and the business owner is unwilling to take money from their marketing budget (or any other budget) to put towards analytics.
Some others answers touched on this but what you need is a case study or customer reference.
If you don't already have customers do a theoretical case study that shows what is measured and how this translated into obvious actionables to improve customer conversion via the website. Hence the common phrase "actionable insights".
Don't under estimate how simple the pitch should be for the customer. Even if they are highly intelligent, the simpler and clearer the value proposition is the more likely you will get a yes. Because then the decision is more of a common sense conclusion and no further thought/time/research required before the sale can happen.