Agreed, this is a typical error because people often don't really understand how Fragments work when they begin working on Android development. To alleviate confusion, I created a simple example code that I originally posted on Application is stopped in android emulator , but I posted it here as well.
An example is the following:
public class ContainerActivity extends FragmentActivity implements ExampleFragment.Callback
{
    @Override
    public void onCreate(Bundle saveInstanceState)
    {
        super.onCreate(saveInstanceState);
        this.setContentView(R.layout.activity_container);
        if (saveInstanceState == null)
        {               
             getSupportFragmentManager().beginTransaction()
                .add(R.id.activity_container_container, new ExampleFragment())
                .addToBackStack(null)
             .commit();
        }
        getSupportFragmentManager().addOnBackStackChangedListener(new OnBackStackChangedListener()
        {
            public void onBackStackChanged()
            {
                int backCount = getSupportFragmentManager().getBackStackEntryCount();
                if (backCount == 0)
                {
                    finish();
                }
            }
        });
    }
    @Override
    public void exampleFragmentCallback()
    {
        Toast.makeText(this, "Hello!", Toast.LENGTH_LONG).show();
    }
}
activity_container.xml:
<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:orientation="vertical" >
    <FrameLayout
        android:id="@+id/activity_container_container"
        android:layout_width="match_parent"
        android:layout_height="match_parent" />
</RelativeLayout>
ExampleFragment:
public class ExampleFragment extends Fragment implements View.OnClickListener
{
    public static interface Callback
    {
        void exampleFragmentCallback();
    }
    private Button btnOne;
    private Button btnTwo;
    private Button btnThree;
    private Callback callback;
    @Override
    public void onAttach(Activity activity)
    {
        super.onAttach(activity);
        try
        {
            this.callback = (Callback) activity;
        }
        catch (ClassCastException e)
        {
            Log.e(this.getClass().getSimpleName(), "Activity must implement Callback interface.", e);
            throw e;
        }
    }
    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState)
    {
        View rootView = inflater.inflate(R.layout.fragment_example, container, false);
        btnOne = (Button) rootView.findViewById(R.id.example_button_one);
        btnTwo = (Button) rootView.findViewById(R.id.example_button_two);
        btnThree = (Button) rootView.findViewById(R.id.example_button_three);
        btnOne.setOnClickListener(this);
        btnTwo.setOnClickListener(this);
        btnThree.setOnClickListener(this);
        return rootView;
    }
    @Override
    public void onClick(View v)
    {
        if (btnOne == v)
        {
            Toast.makeText(getActivity(), "One.", Toast.LENGTH_LONG).show();
        }
        else if (btnTwo == v)
        {
            Toast.makeText(getActivity(), "Two.", Toast.LENGTH_LONG).show();
        }
        else if (btnThree == v)
        {
            callback.exampleFragmentCallback();
        }
    }
}
fragment_example.xml:
<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
        android:layout_width="match_parent"
        android:layout_height="match_parent" >
        <Button
            android:id="@+id/example_button_one"
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:layout_alignParentTop="true"
            android:layout_centerHorizontal="true"
            android:layout_marginTop="30dp"
            android:text="@string/hello" 
            android:layout_marginLeft="20dp"
            android:layout_marginRight="20dp"/>
        <Button
            android:id="@+id/example_button_two"
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_alignLeft="@+id/example_button_one"
            android:layout_alignRight="@+id/example_button_one"
            android:layout_below="@+id/example_button_one"
            android:layout_marginTop="30dp"
            android:text="@string/hello" />
        <Button
            android:id="@+id/example_button_three"
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_alignLeft="@+id/example_button_two"
            android:layout_alignRight="@+id/example_button_two"
            android:layout_below="@+id/example_button_two"
            android:layout_marginTop="30dp"
            android:text="@string/hello" />
</RelativeLayout>
And that should be a valid example, it shows how you can use an Activity to display a Fragment, and handle events in that Fragment. And also how to communicate with the containing Activity.