It is because you have declared String[] strengths which is an array.
declare your constructor like this :
public WeeklyFiber(String sampleID, String weekOfTest, int engineerID, String[] strengths)
{
this.sampleID = sampleID;
this.weekOfTest = weekOfTest;
this.engineerID = engineerID;
this.strengths = strengths;
count++;
}
Make a call like :
WeeklyFiber week2 = new WeeklyFiber("CS4567", "11/24/13", 32, new String[] {"27","26", "28"});