Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Textbook Question
Chapter 5.7, Problem 8E
A candy maker produces mints that have a label weight of 20.4 grams. Assume that the distribution of the weights of these mints is
(a) Let X denote the weight of a single mint selected at random from the production line. Find
(b) During a particular shift, 100 mints are selected at random and weighed. Let Y equal the number of these mints that weigh less than 20.857 grams. Approximate
(c) Let
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As part of a study at a large university, data were collected on n= 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average
(GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
X 1 = average high school grade in mathematics (HSM)
X 2 = average high school grade in science (HSS)
X 3 = average high school grade in English (HSE)
X 4 = SAT mathematics score (SATM)
X5 = SAT verbal score (SATV)
A first-order model was fit to data with R = .193.
Interpret the value of the adjusted coefficient of determination R
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following
independent variables (recorded at the time the students enrolled in the university):
X 1= average high school grade in mathematics (HSM)
X 2 = average high school grade in science (HSS)
X 3 = average high school grade in English (HSE)
X 4 = SAT mathematics score (SATM)
x 5 = SAT verbal score (SATV)
A first-order model was fit to the data with the following results:
SOURCE
DF
MS
F VALUE
PROB>F
MODEL
28.64
5.73
11.69
0001
ERROR
218
106 82
0.49
TOTAL
223
135.46
ROOT MSE
DEP MEAN
0.700
R-SQUARE
0.211
4.635
ADJ R-SQ
0.193
PARAMETER
STANDARD
T FOR O
VARIABLE
ESTIMATE
ERROR
PARAMETER -0
PROB> ITI
INTERCEPT
2.327
0.039
5.817
0.0001
0.0003
XI HSM)
X2 (HSS)
X3 (HSE)
X4 (SATM)
X5 (SATV)
0.146
0.037
3.718
a.036
0.038
0.950
0.3432…
Accountants at the Tucson firm, Larry Youdelman,CPAs, believed that several traveling executives were submittingunusually high travel vouchers when they returned from businesstrips. First, they took a sample of 200 vouchers submitted from
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the road ( x1 ) and distance traveled ( x2 ) in miles:yn = +90.00 + +48.50x1 + +.40x2The coefficient of correlation computed was .68.a) If Donna Battista returns from a 300-mile trip that took herout of town for 5 days, what is the expected amount she shouldclaim as expenses?b) Battista submitted a reimbursement request for $685. Whatshould the accountant do?c) Should any other variables be included? Which ones? Why?
Chapter 5 Solutions
Probability and Statistical Inference (9th Edition)
Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Let X have a gamma distribution with =3 and =2....Ch. 5.1 - The pdf of X is f(x)=2x,0x1. (a) Find the cdf of...Ch. 5.1 - Prob. 5ECh. 5.1 - Let X have a logistic distribution with pdf...Ch. 5.1 - A sum of $50000 is invested at a rate R, selected...Ch. 5.1 - The lifetime (in years) of a manufactured product...Ch. 5.1 - Statisticians frequently use the extreme extreme...Ch. 5.1 - Prob. 10E
Ch. 5.1 - Let X have a Cauchy distribution. Find (a) P(X1)....Ch. 5.1 - Let f(x)=1[(1+x2)],x, be the pdf of the Cauchy...Ch. 5.1 - If X is N(,2), then M(t)=E(etX)=exp(t+2t22),t. We...Ch. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.2 - Let X1,X2, denote two independent random...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Prob. 3ECh. 5.2 - Let the distribution of W be F(9, 24). Find the...Ch. 5.2 - Let the distribution of W be F(8. 4). Find the...Ch. 5.2 - Let X1 and X2 have independent gamma distributions...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Let X have a beta distribution with parameters ...Ch. 5.2 - Determine the constant c such that...Ch. 5.2 - When and are integers and0p1, we have...Ch. 5.2 - Evaluate 00.4(7)(4)(3)y3(1y)2dy (a) Using...Ch. 5.2 - Let W1,W2 be independent, each with a Cauchy...Ch. 5.2 - Let X1, X2 be independent random variables...Ch. 5.2 - Prob. 14ECh. 5.2 - In Example 5.2-6, verify that the given...Ch. 5.2 - Let W have an F distribution with parameters r1...Ch. 5.3 - Let X1 and X2 be a random sample of size n=2 from...Ch. 5.3 - Let X1,X2,X3 be three independent random variables...Ch. 5.4 - Let X1+X2+X3 be a random sample of size 3 from the...Ch. 5.4 - Let X1 and X2 have independent distributions...Ch. 5.4 - Prob. 3ECh. 5.4 - Generalize Exercise 5.4-3 by showing that the sum...Ch. 5.4 - Let Z1,Z2,....,Z7 be a random sample from the...Ch. 5.4 - Let X1,X2,X3,X4,X5 be a random sample of size 5...Ch. 5.4 - Let X1,X2,X3 denote a random sample of size 3 from...Ch. 5.4 - Let W=X1+X2+...+Xh, a sum of h mutually...Ch. 5.4 - Let X and Y, with respective pmfs f(x) and g(y),...Ch. 5.4 - Let X equal the outcome when a fair four-sided die...Ch. 5.4 - Let X and Y equal the outcomes when two fair...Ch. 5.4 - Let X and Y be the outcomes when a pair of fair...Ch. 5.4 - Let X1,X2,...,X8 be a random sample from a...Ch. 5.4 - The number of accidents in a period of one week...Ch. 5.4 - Given a fair four-sided die, let Y equal the...Ch. 5.4 - The number X of sick days taken during a year by...Ch. 5.4 - In a study concerning a new treatment of a certain...Ch. 5.4 - The number of cracks on a highway averages 0.5 per...Ch. 5.4 - A doorman at a hotel is trying to get three taxic...Ch. 5.4 - The time X in minutes of a visit to a...Ch. 5.4 - Let X and Y be independent with distributions...Ch. 5.4 - Let X1 and X2 be two independent random variables....Ch. 5.4 - Let X be N(0,1). Use the mgf technique to show...Ch. 5.5 - Let X1,X2...,X16, be a random sample from a normal...Ch. 5.5 - Let X be N(50,36). Using the same set of axes,...Ch. 5.5 - Let X equal the widest diameter (in millimeters)...Ch. 5.5 - Let X equal the weight of the soap in a 6-pound...Ch. 5.5 - Let X equal the weight (in grams) of a nail of the...Ch. 5.5 - Let X1,X2,...,X100 be a random sample from N(,4),...Ch. 5.5 - Suppose that the distribution of the weight of a...Ch. 5.5 - Let X denote the wing length in millimeters of a...Ch. 5.5 - Suppose that the length of life in hours (say, X)...Ch. 5.5 - A consumer buys n light bulbs, each of which has a...Ch. 5.5 - A marketing research firm suggests to a comp any...Ch. 5.5 - Let the independent random variables X1 and X2 be...Ch. 5.5 - Prob. 13ECh. 5.5 - Let T have at distribution with r degrees of freed...Ch. 5.5 - Let the distribution of T be t(17). 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