Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Honors Statistics
Aug 23-8:26 PM
3. Notes Quiz 5.1
4. Introduce beginning probability ideas
Aug 23-8:31 PM
1
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Nov 9-5:30 PM
Nov 9-5:34 PM
2
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Honors Statistics
Notes Quiz
Chapter 5 Section 1
Nov 1-1:41 PM
Ask me if I have heard the latest Statistics Joke ....
Mrs. Garrett, Have you heard the latest Stats Joke?
probably!!
Nov 13-7:46 AM
3
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Nov 12-11:12 AM
Nov 9-6:00 PM
4
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Nov 9-6:00 PM
Nov 12-11:44 AM
5
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
The real answer
Nov 12-11:47 AM
Mammograms Many women choose to have annual mammograms to screen for
breast cancer after age 40. A mammogram isn’t foolproof. Sometimes the test
suggests that a woman has breast cancer when she really doesn’t (a “false positive”).
Other times the test says that a woman doesn’t have breast cancer when she actually
does (a “false negative”). Suppose the false negative rate for a mammogram is 0.10.
(a) Interpret this probability as a long-run relative frequency.
(b) Which is a more serious error in this case: a false positive or a false negative?
Justify your answer.
A) If we test many, many women with breast cancer, about 10%
of the time the results will say that the woman does not have
breast cancer.
B) I believe a false negative is much more serious. A woman would think
that she does not have cancer when in fact she actually does. This means
she will miss out on getting early treatment with could cause the cancer to
grow and become more serious. A false positive will be bad as well but just
more scary. A woman may be lead to believe that she has breast cancer
when she does not ... she will be anxious until the next test shows a true
negative.
Nov 12-8:34 AM
6
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Nov 9-6:01 PM
Nov 9-6:01 PM
7
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
A SKIPS 3 and 7
Apr 25-10:55 AM
Liar, liar! Sometimes police use a lie detector (also known as a polygraph) to
help determine whether a suspect is telling the truth. A lie detector test isn’t
foolproof—sometimes it suggests that a person is lying when he or she is
actually telling the truth (a “false positive”). Other times, the test says that the
suspect is being truthful when the person is actually lying (a “false negative”). For
one brand of polygraph machine, the probability of a false positive is 0.08.
(a) Interpret this probability as a long-run relative frequency.
If we were to test many many people who would only ever tell
the truth (Yes we have programmed them to only tell the
truth). This polygraph machine would suggest 8% of these
truth teller are lying. (when they really aren't)
(b) Which is a more serious error in this case:
a false positive or a false negative? Justify your answer.
I think that this answer depends on the situation. In this
country we assume you are innocent until proven guilty. A
false positive would call someone a liar who really is not ...
If it is a really serious crime, then a false negative would
allow a criminal to be "telling the truth" and could be found
not quilty of a serious crime.
Nov 12-8:30 AM
8
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Genetics Suppose a married man and woman both carry a gene for cystic
fibrosis but don’t have the disease themselves. According to the laws of
genetics, the probability that their first child will develop cystic fibrosis is
0.25.
(a) Explain what this probability means.
If it were possible for the couple to have many, many first
born children .... then approximately 25% of these "first" borns
would have cystic fibrosis. OR If we were to survey many,
many families that have this same probability, approximately
25% of them would have a first born child with cystic fibrosis.
(b) If the couple has 4 children, is one of them guaranteed to get cystic
fibrosis? Explain.
No this is not guaranteed. This is stated as a probability for
only the first born child. Secondly, if the probability does
apply to all the children ... then if the couple had many, many
childern approximately 25% of them would have cystic fibrosis.
Nov 12-8:35 AM
Texas hold ’em In the popular Texas hold ‘em variety of poker, players
make their best five-card poker hand by combining the two cards they
are dealt with three of five cards available to all players. You read in a
book on poker that if you hold a pair (two cards of the same rank) in
your hand, the probability of getting four of a kind is 88/1000.
(a) Explain what this probability means.
If one were to play Texas Hold'em many, many times for a very long
while, one would hold a pair or two cards of the same rank
approximately 88/1000.
(b) If you play 1000 such hands, will you get four of a kind in exactly
88 of them? Explain.
No. This is not a "long" enough "in the long run".The
number of hands that you get four of a kind could be
smaller or larger than a random chance of 88/1000.
Nov 12-8:35 AM
9
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Spinning a quarter With your forefinger, hold a new quarter (with
a state featured on the reverse) upright, on its edge, on a hard
surface. Then flick it with your other forefinger so that it spins for
some time before it falls and comes to rest. Spin the coin a total
of 25 times, and record the results.
(a) What’s your estimate for the probability of heads? Why?
Not knowing anything about coin "gambling" I would guess
around 50%.
(b) Explain how you could get an even better estimate.
Do this "experiment" spin the coin many, many more
times.
Nov 12-8:44 AM
Nickels falling over You may feel it’s obvious that the probability of a head in
tossing a coin is about 1/2 because the coin has two faces. Such opinions are
not always correct. Stand a nickel on edge on a hard, flat surface. Pound the
surface with your hand so that the nickel falls over. Do this 25 times, and record
the results.
(a) What’s your estimate for the probability that the coin falls heads up? Why?
Not knowing anything about coin "gambling" I would guess
around 50%.
(b) Explain how you could get an even better estimate.
Do this "experiment" slam the coin many, many more
times.
Nov 12-8:44 AM
10
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Free throws The figure below shows the results of a
virtual basketball player shooting several free throws.
Explain what this graph says about chance behavior in the
short run and long run.
In the short run there is a lot of
"wiggling" variability. But in the
long run the graph seems to be
leveling off around 30%. (after
many more attempts.
Nov 12-8:45 AM
Keep on tossing The figure below shows the
results of two different sets of 5000 coin
tosses. Explain what this graph says about
chance behavior in the short run and the
long run.
It appears that the two tosses are
very unpredictable at the begin of the
activity. However as the number of
tosses increase. The long run
probability is stabilizing around the
particular value of 50%
Nov 12-8:45 AM
11
Chapter 5 Section 1 day 1 2016s Notes.notebook
April 11, 2016
Due for a hit A very good professional baseball player gets a hit
about 35% of the time over an entire season. After the player failed to
hit safely in six straight at-bats, a TV commentator said, “He is due
for a hit by the law of averages.” Is that right? Why?
Six is not Many, Many ....
No he is incorrectly applying the law of averages to a small
number of at bats (six) ... the player could also be hurt which
will eventually change his batting average ... in the long run!
Nov 12-8:46 AM
Cold weather coming A TV weather man, predicting a colder-than-normal
winter, said, “First, in looking at the past few winters, there has been a lack
of really cold weather. Even though we are not supposed to use the law of
averages, we are due.” Do you think that “due by the law of averages”
makes sense in talking about the weather? Why or why not?
Past few winters is not many, many ...
I believe that there are many, many variables that go into
weather predicting. Most importantly what the weather is
doing currently should be the best factor in prediciting the
future. He is using the law of averages and the law of
large numbers (by only using a few past winters) in the
wrong way.
Nov 12-8:46 AM
12