Hypothesis Testing - Median Test for linear regression model given standard error and co-efficient

I need help approaching this particular problem on hypothesis testing.

A researcher believes that a diet high in raw cornstarch would increase the median blood glucose levels by 20. The diet can either be high in raw cornstarch (have a value of 1) or low in cornstarch (have a value of 0); let’s call this feature x. To test the researcher’s hypothesis, say I build a linear regression model with x as a covariate and the coefficient associated with raw cornstarch is 2.76 with a standard error of 0.78. How can I compute if there is evidence to reject the researcher’s claim?
And how can I defend this analysis with someone who has no knowledge of linear models?