Check box that creates nested objects in rails

I'm building an app that creates exams. For the part where a user selects the answers on the exam, I want to use a checkbox (or a radio button) to allow them to pick the answer.

I want all the user-selected answers to be a table in itself called "responses". I can't figure out how to use a radio button to create records.

All the response record needs to do is take the ID's of the Exam, User, and Score. Score is a table that tracks the user's scores and the number of correct answers. Here's my examination model (rails wouldn't let me use the word "exam"). I have it set for nested attributes.

class Examination < ApplicationRecord
  belongs_to :user
  has_many :questions, dependent: :destroy
  has_many :scores
  has_many :responses
  has_secure_password

  accepts_nested_attributes_for :responses, allow_destroy: true
end

The response model is pretty basic:

class Response < ApplicationRecord
  belongs_to :user
  belongs_to :score
  belongs_to :examination
end

Here's the "take an exam" page: <%= link_to "Back to all exams", examinations_path %>

<h2><%= @exam.name %></h2>
<h3><%= @exam.intro %></h3>

<%= form_for @exam  do |f| %>
  <%= f.hidden_field :name, value: @exam.name  %>
  <%= fields_for :responses do |res_f| %>
    <% @exam.questions.each_with_index do |question, i| %>
      <% index = i + 1 %>
      <h2>Question #<%=index%></h2><span style="font-size: 24px; font-weight: normal">(<%= question.points %> Points)</span>
      <hr>
      <h3><%= question.body %></h3>
      <% question.answers.each do |ans| %>
        <table>
          <tr>
            <td><%= res_f.check_box :answer_id , ans.id, :examination_id , @exam.id, :user_id  %></td>
            <td><%= ans.body %></td>
          </tr>
        </table>
      <% end %>
    <% end %>
  <% end %>

  <%= f.submit 'Submit' %>
<% end %>

This code doesn't run because Rails expects the responses records to exist in order to use the form. It throws this error:

undefined method `merge' for 484:Integer

If I tweak that checkbox code to this:

<%= res_f.check_box :answer_id  %>

The code will run and it will give me the following params on submit:

Started PATCH "/examinations/34" for 127.0.0.1 at 2018-02-24 16:22:41 -0800
Processing by ExaminationsController#update as HTML
      Parameters: {"utf8"=>"✓", "authenticity_token"=>"y4vcPByUKnDdM6NsWDhwxh8MxJLZU4TQo+/fUrmKYEfb3qLn5FVieJAYirNRaSl0w5hJax20w5Ycs/wz1bMEKw==", "examination"=>{"name"=>"Samuel Smith’s Oatmeal Stout"}, "responses"=>{"answer_id"=>"1"}, "commit"=>"Submit", "id"=>"34"}

I know it's not right but I was hoping it would create a record at least. All the checkbox has to do it create a response record. It should be able to grab the answer_id, exam_id and user_id. That's it.

Does anyone know how to do this?