Transcript File - phsapstatistics

WARM – UP
1. A two sample t-test analyzing if there was a
significant difference between the cholesterol level
of men on a NEW medication vs. the traditional
yields a p-value of 0. DEFINE p-value in context a
problem.
P-Value = the Probability that you would obtain x or pˆ or
even more extreme results given the assumption H0 is True.
“There is a zero chance of seeing a difference between the
two medications given the two drugs are actually equally
effective.”
Warm – Up (continued…)
2. What does a Significance level of 0.05 mean?
α = 0.05 means you would only obtain these results 5 out of
100 times or 1 time out of every 20 samples. RARE!!
Chapter 14 - PROBABILITY
We call a phenomenon RANDOM if individual outcomes are
uncertain.
The PROBABILITY of any outcome is the proportion of times
the outcome would occur in a very long series of
Independent repetitions or trials. Relative Frequency.
An EVENT = P(A)
The Law of Large Numbers says that the long-run relative
frequency of repeated independent events settles down to the
true probability as the number of trials increase.
If you flip a fair coin 19 times and it come up tails. What is
the probability that it will be tails on the 20th flip?
Many people believe in The Law of Averages in which they
feel that in the short term random phenomena is supposed to
compensate somehow for whatever happened in the past.
PROBABILITY MODELS
The SAMPLE SPACE, S, of a random phenomenon is the
set of all possible outcomes.
EXAMPLE: List the sample space for the event of tossing a
coin and roll one die.
S = { H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 }
MULTIPLICATION PRINCIPLE If one event can be done
‘a ‘ ways and another event ‘b’ ways, then the total number
of outcomes in the sample space = a x b .
EXAMPLE: What is the probability of tossing a coin and getting
“heads” 5 times in a roll?
1 1 1 1 1
   
2 2 2 2 2
1

 0.03125
32
EXAMPLE: A 6 question multiple choice test has four answer
choices for each question. If you are completely unprepared,
what is the probability that you will get all 6 questions correct?
1 1 1 1 1 1
1
    

4 4 4 4 4 4
4096
 0.000244
What is the Probability of rolling a die and getting a “1” three
times in a row?
1 1 1
1
 

 0.0046
P(1 and 1 and 1) =
6 6 6
216
What is the Probability of rolling a die and NOT getting a “1”
at all in three roles?
P(Not 1 and Not 1 and Not 1) =
5 5 5
125
 0.8333
 

6 6 6
216
Chapter 14 - More Probability
PROBABILITY RULES:
1.The Probability of P(A) is always: 0 ≤ P(A) ≤ 1 .
2.The Probability of every event in the Sample Space
together is equal to one. P(S) = 1 .
3.The Complement of any event is the Probability that the
event will NOT occur.
P(Ac) = 1 – P(A) .
4.Two events A and B are Disjoint if they have no
outcomes in common and so can never occur
simultaneously. The Addition Rule for disjoint events is:
P(A or B) = P(A) + P(B).
Sample spaces can also be modeled by TREE DIAGRAMS.
EXAMPLE: List the sample space for the event of tossing a
coin and roll one die.
H
T
1
2
3
4
5
6
1
2
3
4
5
6
What is the Probability of Tossing a coin, getting “TAILS” and
then rolling a die and getting an “ODD” number?
3
1
P(TAIL and ODD#) =

12
4
• Textbook: Page 339: 1-6, 8
1. Roulette. If a roulette wheel is to be considered truly random, then
each outcome is equally likely to occur, and knowing one outcome
will not affect the probability of the next. Additionally, there is an
implication that the outcome is not determined through the use of
an electronic random number generator.
2. Rain. When a weather forecaster makes a prediction such as a 25%
chance of rain, this means that when weather conditions are like
they are now, rain happens 25% of the time in the long run.
3. Winter. Although acknowledging that there is no law of averages,
Knox attempts to use the law of averages to predict the severity of
the winter. Some winters are harsh and some are mild over the long
run, and knowledge of this can help us to develop a long-term
probability of having a harsh winter. However, probability does not
compensate for odd occurrences in the short term. Suppose that the
probability of having a harsh winter is 30%. Even if there are several
mild winters in a row, the probability of having a harsh winter is still
30%.
• Textbook: Page 339: 1-6, 8
4. Snow. The radio announcer is referring to the “law of averages”,
which is not true. Probability does not compensate for deviations
from the expected outcome in the recent past. The weather is not
more likely to be bad later on in the winter because of a few sunny
days in autumn. The weather makes no conscious effort to even
things out, which is what the announcer’s statement implies.
5. Cold streak. There is no such thing as being “due for a hit”. This
statement is based on the so-called law of averages, which is a
mistaken belief that probability will compensate in the short term for
odd occurrences in the past. The batter’s chance for a hit does not
change based on recent successes or failures.