typo

<?php
class wctest{
    public function __construct(){
        if(is_admin()){
        add_action('admin_menu', array($this, 'add_plugin_page'));
        add_action('admin_init', array($this, 'page_init'));
    }
    }

    public function add_plugin_page(){
        // This page will be under "Settings"
    add_options_page('Settings Admin', 'Settings', 'manage_options', 'test-setting-admin', array($this, 'create_admin_page'));
    }

    public function create_admin_page(){
        ?>
    <div class="wrap">
        <?php screen_icon(); ?>
        <h2>Settings</h2>
        <form method="post" action="options.php">
            <?php
                    // This prints out all hidden setting fields
            settings_fields('test_option_group');
            do_settings_sections('test-setting-admin');
        ?>
            <?php submit_button(); ?>
        </form>
    </div>
    <?php
    }

    public function page_init(){
    register_setting('test_option_group', 'array_key', array($this, 'check_ID'));

        add_settings_section(
        'setting_section_id',
        'Setting',
        array($this, 'print_section_info'),
        'test-setting-admin'
    );

    add_settings_field(
        'some_id',
        'Some ID(Title)',
        array($this, 'create_an_id_field'),
        'test-setting-admin',
        'setting_section_id'
    );
    }

    public function check_ID($input){
        if(is_numeric($input['some_id'])){
        $mid = $input['some_id'];
        if(get_option('test_some_id') === FALSE){
        add_option('test_some_id', $mid);
        }else{
        update_option('test_some_id', $mid);
        }
    }else{
        $mid = '';
    }
    return $mid;
    }

    public function print_section_info(){
    print 'Enter your setting below:';
    }

    public function create_an_id_field(){
        <input type="text" id="input_whatever_unique_id_I_want" name="array_key[some_id]" value="get_option('test_some_id');" />
    }
}

$wctest = new wctest();

?>