Quiz 3

As a 4-H project, Billy is raising chickens. He feeds and waters them every day, and collects the eggs every other day, selling them to people in the neighborhood.  He has found that each hen's nest will contain from 0 to 2 eggs. Based on past experience he estimates that there will be no eggs in 10% of the nests, one egg in 30% of the nests, 2 eggs in the other 60%.  Conduct a simulation to estimate how many nests Billy will have to visit to collect a dozen eggs.

1. Describe how you will use a random number table to conduct this simulation.

Here you describe how you will assign digits in the random number table to outcomes of the "experiment".  You should assign 1 of the digits to represent finding no eggs, three of the digits to finding 1 egg, and the rest to finding 2.  For example, let 0 == no eggs, 1,2,3 == find 1 egg, and 4,5,6,7,8,9 == find 2 eggs.

2. Show three trials by clearly labeling the random number table given below.  Specificy the outcome for each trial.

   Random  Numbers:  5 7 5 2 8    7 8 xxxx one trial (13 eggs) xxxx3 0 5 6 3 5 0 8 2 9 xxxone trial (13 eggs) 4 1 8 9 0 6 7 6 xxx one trial (13 eggs) 

   We can stop now, because we've done 3 trials. A trial consists of collecting eggs until you've collected a dozen.  In these trials, we always ended up with just over a dozen.

A common mistake was to do too many trials -- to use up all of the random numbers.  But you were only asked for three.  If you did more, then we might wonder whether you knew what a trial was.   You could help us here but saying that you deliberately did more than 3 and telling us how many you did.  But easier to stop at 3.

Another mistake was to skip numbers.  Don't do this, or we'll assume you're reading the table wrong. Stick to your plan outlined in number 1.

In the first trial it took 7 nests.  In the second it took 10 tests.  In the third 8.  

3. State your conclusion.

It doesn't make sense to do a graphic for just three observations.  But you should use a summary statistic -- either median or mean.  Let's take the mean, which is 8.3.  This means that it takes, on average, 8.3 nests to get at least a dozen eggs.  

Common mistakes -- several people said "the mode was at 8 nests".  The mode is the value that occurs most frequently.  there is no mode here because all three values, 7,8,10, occurr the same number of times.

Other mistakes:  Some people didn't do enough nests.  They stopped at 5 because the random numbers were in groups of 5.  The random numbers are grouped that way for your convenience. Before you begin, think about what constitutes one complete trial of the experiment. In this case, a trial is not completed until you've collected 12 eggs.

"You'd have to visit about 8 nests, assuming that everythign else is normal dn the hen's lay their eggs normally."  Not sure what normally means here, but if you mean "according to the normal curve" then this is wrong.  First, the distribution of the number of eggs laid is NOT normal. Second, this assumption doesn't matter here.  8 is the average no matter what the distribution is.

"Out of twelve nests there is a good chance at getting a dozen eggs".  This one makes the mistake of taking numbers in groups of 12 and seeing if there are 12 eggs.  Read the problem closely and make sure you answer the right question.

"About 60% of the time the nests will have 2 eggs."  Again, right answer to the wrong question.