Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 8, Problem 73SE
To determine
Test whether more than 10% of the population sampled had completely abstained from alcohol use.
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Consider the ceocomp dataset of compensation information for the CEO’s of 100 U.S. companies. We wish to fit aregression model to assess the relationship between CEO compensation in thousands of dollars (includes salary andbonus, but not stock gains) and the following variates:AGE: The CEOs age, in yearsEDUCATN: The CEO’s education level (1 = no college degree; 2 = college/undergrad. degree; 3 = grad. degree)BACKGRD: Background type(1= banking/financial; 2 = sales/marketing; 3 = technical; 4 = legal; 5 = other)TENURE: Number of years employed by the firmEXPER: Number of years as the firm CEOSALES: Sales revenues, in millions of dollarsVAL: Market value of the CEO's stock, in natural logarithm unitsPCNTOWN: Percentage of firm's market value owned by the CEOPROF: Profits of the firm, before taxes, in millions of dollars1) Create a scatterplot matrix for this dataset. Briefly comment on the observed relationships between compensationand the other variates.Note that companies with negative…
6 (Model Selection, Estimation and Prediction of GARCH) Consider the daily returns rt
of General Electric Company stock (ticker: "GE") from "2021-01-01" to "2024-03-31",
comprising a total of 813 daily returns. Using the "fGarch" package of R, outputs of
fitting three GARCH models to the returns are given at the end of this question.
Model 1 ARCH (1) with standard normal innovations;
Model 2
Model 3
GARCH (1, 1) with Student-t innovations;
GARCH (2, 2) with Student-t innovations;
Based on the outputs, answer the following questions.
(a) What can be inferred from the Standardized Residual Tests conducted on Model 1?
(b) Which model do you recommend for prediction between Model 2 and Model 3?
Why?
(c) Write down the fitted model for the model that you recommended in Part (b).
(d) Using the model recommended in Part (b), predict the conditional volatility in the
next trading day, specifically trading day 814.
4 (MLE of ARCH) Suppose rt follows ARCH(2) with E(rt) = 0,
rt = ut, ut =
στει, σε
where {+} is a sequence of independent and identically distributed (iid) standard normal
random variables.
With observations r₁,...,, write down the log-likelihood function for the model esti-
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Chapter 8 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 8.1 - For each of the following assertions, state...Ch. 8.1 - For the following pairs of assertions, indicate...Ch. 8.1 - For which of the given P-values would the null...Ch. 8.1 - Pairs of P-values and significance levels, , are...Ch. 8.1 - To determine whether the pipe welds in a nuclear...Ch. 8.1 - Let denote the true average radioactivity level...Ch. 8.1 - Before agreeing to purchase a large order of...Ch. 8.1 - Many older homes have electrical systems that use...Ch. 8.1 - Water samples are taken from water used for...Ch. 8.1 - A regular type of laminate is currently being used...
Ch. 8.1 - Prob. 11ECh. 8.1 - A mixture of pulverized fuel ash and Portland...Ch. 8.1 - The calibration of a scale is to be checked by...Ch. 8.1 - A new design for the braking system on a certain...Ch. 8.2 - Let denote the true average reaction time to a...Ch. 8.2 - Newly purchased tires of a particular type are...Ch. 8.2 - Answer the following questions for the tire...Ch. 8.2 - Reconsider the paint-drying situation of Example...Ch. 8.2 - The melting point of each of 16 samples of a...Ch. 8.2 - Lightbulbs of a certain type are advertised as...Ch. 8.2 - The desired percentage of SiO2 in a certain type...Ch. 8.2 - To obtain information on the corrosion-resistance...Ch. 8.2 - Automatic identification of the boundaries of...Ch. 8.2 - Unlike most packaged food products, alcohol...Ch. 8.2 - Body armor provides critical protection for law...Ch. 8.2 - Prob. 26ECh. 8.2 - Show that for any 0, when the population...Ch. 8.2 - For a fixed alternative value , show that () 0 as...Ch. 8.3 - The true average diameter of ball bearings of a...Ch. 8.3 - A sample of n sludge specimens is selected and the...Ch. 8.3 - The paint used to make lines on roads must reflect...Ch. 8.3 - The relative conductivity of a semiconductor...Ch. 8.3 - The article The Foremans View of Quality Control...Ch. 8.3 - The following observations are on stopping...Ch. 8.3 - The article Uncertainty Estimation in Railway...Ch. 8.3 - Have you ever been frustrated because you could...Ch. 8.3 - The accompanying data on cube compressive strength...Ch. 8.3 - A random sample of soil specimens was obtained,...Ch. 8.3 - Reconsider the accompanying sample data on expense...Ch. 8.3 - Polymer composite materials have gained popularity...Ch. 8.3 - A spectrophotometer used for measuring CO...Ch. 8.4 - Prob. 42ECh. 8.4 - Prob. 43ECh. 8.4 - A manufacturer of nickel-hydrogen batteries...Ch. 8.4 - A random sample of 150 recent donations at a...Ch. 8.4 - It is known that roughly 2/3 of all human beings...Ch. 8.4 - The article Effects of Bottle Closure Type on...Ch. 8.4 - With domestic sources of building supplies running...Ch. 8.4 - A plan for an executive travelers club has been...Ch. 8.4 - Each of a group of 20 intermediate tennis players...Ch. 8.4 - A manufacturer of plumbing fixtures has developed...Ch. 8.4 - In a sample of 171 students at an Australian...Ch. 8.5 - Reconsider the paint-drying problem discussed in...Ch. 8.5 - Consider the large-sample level .01 test in...Ch. 8.5 - Consider carrying out m tests of hypotheses based...Ch. 8.5 - Prob. 56ECh. 8 - A sample of 50 lenses used in eyeglasses yields a...Ch. 8 - In Exercise 57, suppose the experimenter had...Ch. 8 - It is specified that a certain type of iron should...Ch. 8 - One method for straightening wire before coiling...Ch. 8 - Contamination of mine soils in China is a serious...Ch. 8 - The article Orchard Floor Management Utilizing...Ch. 8 - The article Caffeine Knowledge, Attitudes, and...Ch. 8 - Annual holdings turnover for a mutual fund is the...Ch. 8 - The true average breaking strength of ceramic...Ch. 8 - Prob. 66SECh. 8 - The incidence of a certain type of chromosome...Ch. 8 - Prob. 68SECh. 8 - Prob. 69SECh. 8 - The Dec. 30, 2009. the New York Times reported...Ch. 8 - When X1, X2,, Xn are independent Poisson...Ch. 8 - An article in the Nov. 11, 2005, issue of the San...Ch. 8 - Prob. 73SECh. 8 - The article Analysis of Reserve and Regular...Ch. 8 - Prob. 75SECh. 8 - Chapter 7 presented a CI for the variance 2 of a...Ch. 8 - Prob. 77SECh. 8 - When the population distribution is normal and n...Ch. 8 - Let X1, X2, Xn be a random sample from an...Ch. 8 - Because of variability in the manufacturing...
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