Stat-285 Assignment 10 2007 Fall Term
1. AR(2) Process
Consider an AR(2) process:
Yt = 1 Yt1 + 2 Yt2 + +
where
t
t
is i.i.d N(0, 2 ).
(a) Derive that the mean is:
=
1 1 2
Solution: Start by taking expectations of both sides.
E[Yt ] = 1 E[Yt1 ] + 2 E[Yt2 ]
Mean or median?
Middletown is considering a new tax. The government wants to know
the average income of its citizens so that it can estimate its tax base.
Mean, since a (constant) tax can apply to all incomes, no matter how
small or large
In a study of t
Covered chapters 1-18 and 20-22
Chapter 1-9 covered issues involved in producing data
Chapters 1-4 Introduces different types of sampling and also
variability from sample to sample
Chapters 5-9 introduces experiments and argues that they
are better than
A study looked at a variety of countries and measured the annual
wine consumption (liters of wine consumed per person) and the death
rate from heart disease (number of deaths per 100,000 people) in
2001.
A least-squares regression analysis for the data w
Amount of fat was measured for a random sample of 35 hamburgers
of a particular restaurant chain
It is known from previous studies that the standard deviation of the fat
content is 3.8 grams
Sample mean was found to be 30.2 (no mention of normality)
Find
If the null hypothesis is true, the distribution of the sample proportion
is:
If null hypothesis is true, distribution of phat is approx normal
with a mean of 0.5 and SD of LOOK AT PREVIOUS SLIDES
What does extreme mean in this case? Larger than 0.5
P-Va
It is the thought that counts: Do people value gifts from others
more than cash? We like to think so.
A survey of 209 people asked, If, without the gift-giver ever knowing,
you could receive the monetary value instead of the gift, would you
prefer the mo
How do we interpret significance level view this as the cut-off for
when things can or cannot occur by chance variation
Common sig. Levels 0.10, 0.05, and 0.01 (0.05 is the most common)
Have we proven H0 is true or false? No, conclusion is only made
base
Hypothesis:
Hnot = p=0.10
H1 = p is not equal to 0.1
Our estimate: phat = 15/50 = 0.30
P-Value
Phat=0.3, SD if Hnot is true is sqrt(p(1-p)/n), n=50, p=0.1
SD = Sqrt(0.1(1-0.1)/50) = 0.04
Standard score = 0.30-0.10/0.04 = 5
So p-value is two times the pro
Sales of coffee: Weekly sales of regular ground coffee at a
supermarket have in the recent past varied according to a Normal
distribution with a mean of 354 units per week and a standard
deviation of 33 units.
The store reduces the price by 5%. The sampl
Problem #7
Solution
5
Problem #4
Solution
Problem #5
Solution
Problem #6
Applying the Thompson test to the data of Problem # 1 to see if any of the data points
can be rejected.
Solution
From problem # 2
4
Chapter VI Statistical Analysis of Experimental Data
Sample space: The set of all possible outcomes of an experiment is called the sample
space. Is can be a discrete sample space of a continuous sample space.
Random variable: It is a variable that will ch
Which device would you choose? Explain your answer.
Solution
Problem #6: Digital voltmeters often have a choice of ranges. The ranges indicated on a
typical voltmeter are 0-3, 0-30, 0-300, 0-3000 AC volts. The output is represented with
four significant d
Problem #3
Solution
3
Chapter VI Statistical Analysis of Experimental Data
functions for discrete random variables . For continuous random variables, these
functions are called probability density functions.
- Probability mass function:
n
P( xi ) 1 ;
i 1
Chapter VI Statistical Analysis of Experimental Data
The above bell shaped curve of the histogram is typical of experimental data
(although this is not a rule, see figure 6.2 for other types of histograms).
Figure 6.2. Different distributions of data. a)
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Chapter VI Statistical Analysis of Experimental Data
Figure 6.4. Standard normal density function.
We can write now the above integral in terms of z:
z2
P ( x1
x
x2 )
P( z1
z
z2 )
f z dz
z1
The probability that a measurement will fall in one of more stand
Looked at confidence intervals
Have to know what the confidence interval is giving you from
A technical standpoint How to compute one, assumptions,
explain what the confidence level means, the impact of sample
size, need for central limit theorem
A pract