Transcript 34. INTRODUCING SAMPLING DISTRIBUTION

Sampling Distribution
WELCOME to INFERENTIAL STATISTICS
Types of Distribution
 Frequency
Distribution
 Normal
(Gaussian)
Distribution
 Probability
 Poisson
 Binomial
Distribution
Distribution
 Sampling

Distribution
Distribution
t distribution
AP EXPECTATIONS
COMPLETE WORK ON TIME, EVERY TIME
KEEP YOUR NOTES ORGANIZED
SHOW MATURITY
BE RESPONSIBLE
Am I an AP Statistics student material?
QUESTION 1
On a 10-item multiple-choice quiz
with 4 choices, what is the probability
that you will get 7 of the problems
correctly by guessing
QUESTION 2
According to ACCU Weather, the
chance of raining in Barstow from
Monday-Friday is 43%. What is
the probability that it will rain from
Monday till Wednesday?
QUESTION 3
Shelby is a high school basketball
player(yeah right). She is a 70% free
throw shooter. During this season, what is
the probability that Shelby miss her free
throw on her 4th free throw shot?
QUESTION 4
With a 70% accuracy, how many shots do
you think Shelby is expected to contribute
to his team given that she gets to do 24
free throw shot in this game?
QUESTION 5
Austin needs to get a 1 on his 5th roll to
beat Krista on the game of Monopoly.
What is the probability that Austin keeps
his title on the game of monopoly?
QUESTION 6
What is the expected number of
rolls before a 1 come out in this
monopoly match?
QUESTION 7
What is the difference between
geometric distribution and binomial
distribution?
answers
1. P(x=7) .0030 or .30%
2. P(x≤3) .8878 or 88.78%
3. P(x=4) .0189 or 1.89%
4. µ=np (.70)(20) = 14 shots
5. P(x=5) .0804 or 8.04%
6. µ= 5 rolls
7. Binomial distribution has definite number of trials
What is Sampling Distribution?
•A
sampling distribution is created by, as
the name suggests, sampling.
•The
method we will employ on the rules of
probability and the laws of expected value
and variance to derive the sampling
distribution.
•For
example, consider the roll of one and
A fair die is thrown infinitely many times,
with the random variable X = # of spots on any throw.
The probability distribution of X is:
x
P(x)
1
2
3
4
5
6
1/6
1/6
1/6
1/6
1/6
1/6
…and the mean and variance are calculated as well:
Sampling Distribution of Two Dice
A sampling distribution is created by looking at
all samples of size n=2 (i.e. two dice) and their means…
While there are 36 possible samples of size 2, there are
only 11 values for , and some (e.g. =3.5) occur more
frequently than others (e.g. =1).
Sampling Distribution of Two Dice…
sampling distribution of
6/36
P( )
)
5/36
4/36
P(
•The
3/36
2/36
1/36
is shown below:
Compare the distribution of X…
…with the sampling distribution of
.
The 4 features of sampling
distribution include:
1) The statistic of interest (Proportion, SD, or Mean)
2) Random selection of sample
3) Size of the random sample (very important)
4) The characteristics of the population being
sampled.
Statistic vs. parameter
A statistic is a quantity
that is calculated from a
sample of data
x, s, p
A parameter is a value,
usually unknown (and
which therefore has to
be estimated), used to
represent a certain
population characteristic
 p
In real life parameters of populations are unknown and unknowable.
–For example, the mean height of US adult (18+) men is unknown and unknowable
PARAMETER VS. STATISTIC
 In
real life parameters of populations are
unknown and unknowable.
– For
example, the mean height of US adult (18+) men
is unknown and unknowable
 Rather
than investigating the whole population,
we take a sample, calculate a statistic related to
the parameter of interest, and make an inference.
 The
sampling distribution of the statistic is the
tool that tells us how close the value of the
statistic is to the unknown value of the parameter.