Is there already a StopWatch class for android and why doesn't my implementation work?

Have a look at the Chronometer class.

Sample code from APIDemo:

import android.app.Activity;
import android.os.Bundle;
import android.os.SystemClock;
import android.view.View;
import android.view.View.OnClickListener;
import android.widget.Button;
import android.widget.Chronometer;

public class ChronometerDemo extends Activity {
    Chronometer mChronometer;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);

        setContentView(R.layout.chronometer);

        Button button;

        mChronometer = (Chronometer) findViewById(R.id.chronometer);

        // Watch for button clicks.
        button = (Button) findViewById(R.id.start);
        button.setOnClickListener(mStartListener);

        button = (Button) findViewById(R.id.stop);
        button.setOnClickListener(mStopListener);

        button = (Button) findViewById(R.id.reset);
        button.setOnClickListener(mResetListener);

        button = (Button) findViewById(R.id.set_format);
        button.setOnClickListener(mSetFormatListener);

        button = (Button) findViewById(R.id.clear_format);
        button.setOnClickListener(mClearFormatListener);
    }

    View.OnClickListener mStartListener = new OnClickListener() {
        public void onClick(View v) {
            mChronometer.start();
        }
    };

    View.OnClickListener mStopListener = new OnClickListener() {
        public void onClick(View v) {
            mChronometer.stop();
        }
    };

    View.OnClickListener mResetListener = new OnClickListener() {
        public void onClick(View v) {
            mChronometer.setBase(SystemClock.elapsedRealtime());
        }
    };

    View.OnClickListener mSetFormatListener = new OnClickListener() {
        public void onClick(View v) {
            mChronometer.setFormat("Formatted time (%s)");
        }
    };

    View.OnClickListener mClearFormatListener = new OnClickListener() {
        public void onClick(View v) {
            mChronometer.setFormat(null);
        }
    };
}

R.layout.chronometer:

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android" android:orientation="vertical" android:padding="4dip"
    android:gravity="center_horizontal"
    android:layout_width="match_parent"
    android:layout_height="match_parent">

    <Chronometer android:id="@+id/chronometer"
        android:format="@string/chronometer_initial_format"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_weight="0"
        android:paddingBottom="30dip"
        android:paddingTop="30dip"
        />

    <Button android:id="@+id/start"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content" 
        android:text="@string/chronometer_start">
        <requestFocus />
    </Button>

    <Button android:id="@+id/stop"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content" 
        android:text="@string/chronometer_stop">
    </Button>

    <Button android:id="@+id/reset"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content" 
        android:text="@string/chronometer_reset">
    </Button>

    <Button android:id="@+id/set_format"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content" 
        android:text="@string/chronometer_set_format">
    </Button>

    <Button android:id="@+id/clear_format"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content" 
        android:text="@string/chronometer_clear_format">
    </Button>

</LinearLayout>

Add this to Strings.xml

<string name="chronometer_start">Start</string>
<string name="chronometer_stop">Stop</string>
<string name="chronometer_reset">Reset</string>
<string name="chronometer_set_format">Set format string</string>
<string name="chronometer_clear_format">Clear format string</string>
<string name="chronometer_initial_format">Initial format: <xliff:g id="initial-format">%s</xliff:g></string>

You should use a Chronometer.

But anyway, your code can work if you remove the sleep from UI thread.

private final Runnable mRunnable = new Runnable() {
    @Override
    public void run() {
        if (mStarted) {
            long seconds = (System.currentTimeMillis() - t) / 1000;
            statusBar.setText(String.format("%02d:%02d", seconds / 60, seconds % 60));
            handler.postDelayed(runnable, 1000L);
        }
    }

};

private Hanlder mHandler;
private boolean mStarted;

@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    mHandler = new Handler();
}

@Override
protected void onStart() {
    super.onStart();
    mStarted = true;
    mHandler.postDealyed(runnable, 1000L);
}

@Override
protected void onStop() {
    super.onStop();
    mStarted = false;
    mHandler.removeCallbacks(mRunnable);
}

You should use a Chronometer.

Chronometer mChronometer;
mChronometer = (Chronometer) findViewById(R.id.chronometer1);
long timeWhenStopped = 0;

when we stop the chronometer

timeWhenStopped = mChronometer.getBase() - SystemClock.elapsedRealtime();
mChronometer.stop();

the chronometer before starting it

mChronometer.setBase(SystemClock.elapsedRealtime() + timeWhenStopped);
mChronometer.start();

resetting the chronometer

mChronometer.setBase(SystemClock.elapsedRealtime());
timeWhenStopped = 0;