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Material Type: Notes; Class: INTRO TO STATISTICS 1; Subject: STATISTICS; University: University of Florida; Term: Unknown 1989;
Typology: Study notes
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Thought: Vital papers will demonstrate their vitality by moving from where you left them to where you can’t find them.
Today : P. 236 – 240
For tomorrow: Exercises 5.55 , 5.59 , 5.60 , 5.63 , 5.64 , 5.68
For Wednesday: P. 254 – 264, COMPUTER DEMO
For Thursday: Exercises 6.1, 6.3, 6.4. 6.
Last Time :
Working with the Normal distribution Tables to find probabilities Key : DRAW PICTURES
p. 236 – 240
approximated with probabilities based on a Normal distribution with mean and standard deviation
The .5’s are called corrections for continuity.
The largest value of interest gets a little larger (by
.5) to get to edge of box in the binomial histogram.
Smallest values of interest gets a little smaller.
How “large” should
be so that the normal approximation is “good enough” to use? (Figure 5.19, p. 238, p. 240)
0 1 2 3
.......... n-1 n μ−3σ μ+3σ This turns out to be the same as
smaller of
and
What is the probability that there will be a room for
all who show up?
200 201
............................
P( x < 200 )
What is the probability that more than 190 show up?
Ex. Coin tossing. In 10 tosses, approximate the prob. of getting 4,5 or 6 heads.
Note: The exact prob. in this example is 0. (binomial table gives .656). Approx. is very good here, even for
Thought: A truly wise person never plays leap-frog with a unicorn.
Today : P. 254 – 264
For Thursday: Exercises 6.1, 6.3, 6.4. 6.
For Monday : SPRING BREAK!!!
Last Time : Normal Approximation to the Binomial Distribution
smaller of
and
Write probabilities for the binomial variable with the “=” sign.
Use “Continuity Correction.”
There is a probability distribution associated with
This probability distribution is called the SAMPLING
Ex. Consider a spinner that can land on
or
, each
For the spinner,
numbers.
equal to the true population mean
The standard deviation of the sampling distribution
, is equal to popn std dev sample size
Take
observations.
A point estimator for a parameter (Defn. 6.4, p. 261)
a rule or formula telling how to use the use the data in a sample to compute a single number that we intend to be “close” to the value of the population parameter
mean)
(popn. variance).
Estimator
underestimates (^) μ overestimates μ
Biased
Tends to overestimate too often.
If we have two unbiased estimators, prefer the one with the SMALLER standard error.
μ
μ
