Homework 7 Solutions

Ch. 19: 


12.  (a) These students are probably "high achievers"; we know that
they are listed in the "Who's Who Among American High School Students"
book.  So, it's unwise to think that they are representative of the
whole student body.  For instance, it's possible that these students
feel a lot of pressure to keep on excelling, and thus, they resort to
cheating more often than other students do.

     (b) It's not wise to assume that the survey was representative of
all the students listed in the book.  How were the 5,000 students who
received the survey selected?  Also, there could have been
non-response bias, since less than 40% of the students who received
surveys returned them.



Ch. 20:


5.  We can think of a box that has an average of 150 lbs. and a SD
of about 35 lbs.  We make 50 draws from the box and add them up to
represent the combined weight of the 50 people.  (Remember, the
elevator was designed for 4 tons = 8000 lbs.)

        expected sum = 50(150) = 7500
        SE sum = [(50)^0.5][35] is about 247.49

z-score = [8000-7500]/[(35)(50)^0.5] is about 2.02 (but the closest
number on the table is 2.00)

So, chance of exceeding 4 tons is about: (100-95.45)/2 = 2.275%


11.  (a) 357, 340

     (b) 71.4%, 68%

The expected value is computed from the box; the observed value, from
the sample.



Ch. 21:


3.  In the sample, (172+207)/500 = 379/500 = 75.8% of the households
owned cars.  The percentage of households in the town with cars is
estimated as 75.8%, give or take 1.9% or so.


9.  Your net gain is like the sum of 100 draws from a box with 6
tickets marked "$11" and 94 marked "-$1".  The average of the box is
-$0.28, and the SD is about $2.85.  Your net gain will be around -$28,
give or take $28 or so.