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Honors Statistics

Aug 23-8:31 PM

3. Notes Quiz 5.1

4. Introduce beginning probability ideas

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Honors Statistics

Notes Quiz

Chapter 5 Section 1

Nov 13-7:46 AM

Ask me if I have heard the latest Statistics Joke ....

Mrs. Garrett, Have you heard the latest Stats Joke?

probably!!

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The real answer

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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.

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A SKIPS 3 and 7

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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.

(b) Which is a more serious error in this case:

a false positive or a false negative? Justify your answer.

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)

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.

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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.

(b) If the couple has 4 children, is one of them guaranteed to get cystic fibrosis? Explain.

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.

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.

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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?

(b) Explain how you could get an even better estimate.

Do this "experiment" spin the coin many, many more

times.

Not knowing anything about coin "gambling" I would guess

around 50%.

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?

(b) Explain how you could get an even better estimate.

Do this "experiment" slam the coin many, many more

times.

Not knowing anything about coin "gambling" I would guess

around 50%.

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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.

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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%

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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?

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!

Six is not Many, Many ....

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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?

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.

Past few winters is not many, many ...