Should a survey page contain a footer?

We are working on a questionnaire website. The pages consist of a landing page, questionnaire information, the questionnaire, summarised results and a contact information page. All of these currently include a footer, containing mostly legally important information, e.g.:

• a privacy policy,
• a link to contact us for information,
• a copyright text.

Are these necessary on every page? During the questionnaire, I could imagine that showing this information could even be distracting the user from filling in our questionnaire. However, not showing these could lead to distrust.

My current, suggested implementation is: show the footer on every page, but take out as much elements as possible. In this case, I would only keep the copyright text.

Any ideas?