Using jQuery .ajax () method to submit a form in PHP

I am currently working on a form that allows the user to change their password. And I am not very good at jQuery ajax. It seems like ajax is not sending data to changepassword.php. PHP file works great when I am not using ajax. Can you guys help me here a little?

I have updated my files as per some of the comments. When I try to submit the form, it returns Doesn't Work

. So I think php is responding, but the value didn't make it to the database.

Thanks a lot for helping the guys.

Below is the form and ajax (Updated)

        <form id="form_id" method="POST">
            <label for="username">Username</label>
            <input type="text" name="username" id="username" required />
            <label for="old_password">Old Password</label>
            <input type="password" name="old_password" id="old_password" required />
            <label for="new_password">New Password</label>
            <input type="password" name="new_password" id="new_password" required />
            <button class="submit">
                Submit
            </button>
            <p class="result"></p>
        </form>
        <script>
            $.ajaxSetup({
                cache : false
            });
            $(".submit").click(function(e) {
                $.ajax({
                    url : "changepassword.php",
                    type : "POST",
                    data : $("#form_id").serialize(),
                    success : function(data) {
                        if(data == 1) {
                            $(".result").html("Works");
                        } else {
                            $(".result").html("Doesn't Work");
                        }
                    }
                });
                return false;
            });

        </script>

      

        
        
        
      

    

And this changepassword.php

(Updated)

    <?php
session_start();
ini_set('display_errors', 1);
ini_set('display_startup_errors', 1);
error_reporting(-1);
include_once "../classes/Connect.php";
$connection = new Connect();
$username = $_POST['username'];
$old_password = $_POST['old_password'];
$new_password = $_POST['new_password'];
$result = $connection -> change_password($username, $old_password, $new_password);
if ($result) {
    echo 1;
}
    ?>

      

        
        
        
      

    

This is a method change_password()

from connect.php

a class file

    function change_password($username, $old_password, $new_password){
    $query = "UPDATE Account SET password = ? WHERE username = ? AND password = ?";
    if ($stmt = $this -> conn -> prepare($query)){
        $stmt -> bind_param('sss', md5($new_password), $username, md5($old_password));
        if ($stmt -> execute()){
            return true;
        }
    }
}