android - - java.lang.NullPointerException - setText on null object reference

This is what I'm trying to do for several hours:
I've got a MainActivity.java file (listing below) and a fragment_start.xml file with a start button. Tapping the start-button should display the activity_main.xml file with points-/round- and countdown-Textviews. It doesn't work and this is what is happening:

The logcat tells me:

PID: 1240 java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.TextView.setText(java.lang.CharSequence)' on a null object reference

The emulator displays: Unfortunately, GAME has stopped.

Necessary to mention that I'm rather new in programming?

Thanks for any advice!

import android.app.Activity;
import android.os.Bundle;

import android.view.View;
import android.view.ViewGroup;
import android.widget.TextView;


public class MainActivity extends Activity implements View.OnClickListener {

private int points;
private int round;
private int countdown;


@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);
    showStartFragment();
}

private void newGame () {
    points=0;

    round=1;
    initRound();
}

private void initRound() {
    countdown = 10;
    update();
}

private void update () {

    fillTextView(R.id.points, Integer.toString(points));
    fillTextView(R.id.round, Integer.toString(round));
    fillTextView(R.id.countdown, Integer.toString(countdown * 1000));
}

private void fillTextView (int id, String text) {
    TextView tv = (TextView) findViewById(id);
    tv.setText(text);
}


private void showStartFragment() {
    ViewGroup container = (ViewGroup) findViewById(R.id.container);
    container.removeAllViews();
    container.addView(
            getLayoutInflater().inflate(R.layout.fragment_start, null) );
    container.findViewById(R.id.start).setOnClickListener(this);
}

@Override
public void onClick(View view) {

    if(view.getId() == R.id.start) {
        startGame();
    }
}

public void startGame() {
    newGame();
}
}