Test whether people with a specific genetic marker are more likely to have suffered from clinical depression than people without the genetic marker, using the information that 38% of the 42 people in a sample with the genetic marker have had clinical depression while 12% of the 758 people in the sample without the genetic marker have had clinical depression.

(a) Find the relevant sample proportions in each group and the pooled proportion.
(b) Complete the hypothesis test using the normal distribution and show all details.