how to set dropdown on my setting page

i have add a sub menu under setting page.

i have created two text field but now i want to add dropdown like
1. Yes
2. No

i am trying to do this by the following code but its does not save my value.

printf(

           '<select id="thumbnail" name="my_option_name[thumbnail]" value="%s" ><option selected name="my_option_name[thumbnail]">Yes</option><option name="my_option_name[thumbnail]">No</option></select>',
            isset( $this->options['thumbnail'] ) ? esc_html( $this->options['thumbnail']) : ''
        );