[shell] How to execute a shell script on a remote server using Ansible?

I am planning to execute a shell script on a remote server using Ansible playbook.

blank test.sh file:

touch test.sh

Playbook:

---
- name: Transfer and execute a script.
  hosts: server
  user: test_user
  sudo: yes
  tasks:
     - name: Transfer the script
       copy: src=test.sh dest=/home/test_user mode=0777

     - name: Execute the script
       local_action: command sudo sh /home/test_user/test.sh

When I run the playbook, the transfer successfully occurs but the script is not executed.

It's better to use script module for that:
http://docs.ansible.com/script_module.html

You can use template module to copy if script exists on local machine to remote machine and execute it.

 - name: Copy script from local to remote machine
   hosts: remote_machine
   tasks:
    - name: Copy  script to remote_machine
      template: src=script.sh.2 dest=<remote_machine path>/script.sh mode=755
    - name: Execute script on remote_machine
      script: sh <remote_machine path>/script.sh

you can use script module

Example

- name: Transfer and execute a script.
  hosts: all
  tasks:

     - name: Copy and Execute the script 
       script: /home/user/userScript.sh