Checkbox unchecked after refresh

I have checkboxes on my page, and the default value of all of them is true. However, the select_all checkbox became unchecked after a page refresh while the others remain checked.

<script>
        var $checked = true;
        $('#select_all').click(function() {
                console.log('click select all button'+$checked)
                $checked = !$checked
                $(".activated").each(function(){
                        $(this).prop("checked", $checked)
                });
        });
</script>

<table cellspacing="10">
            <thead>
                    <tr>
                                        <%= check_box_tag 'select_all', 1, true%>
                                        <%= label_tag :select_all, " Select All Doctors" %>
                                </tr>
           </thead>
           <tbody>
                   <tr>
                                 <th>Send Email</th>
                           <th>First Name</th>
                           <th>Last Name</th>
                           <th>Email</th>
                   <% @doctors.each do |doctor| %>
                         <tr>
         <td><%= check_box_tag 'activated[]', doctor.id, true, class: 'activated'%></td>
                                 <td><%= doctor.first_name %></td>
                                 <td><%= doctor.last_name %></td>
                                 <td><%= doctor.email %></td>
                         </tr>
                   <% end %>
           </tbody>
</table>