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 4.3, Problem 5E
Let X and Y have a trinomial distribution with
(a) Give
(b) Compare ‘our answer in part (a) with the equation of the line of best fit in Example 4.2-2. Are they the same? Why or why not?
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We analyze a data set with Y = stopping distance of a car
and X = speed of the car when the brakes were applied,
%3D
and after running the data in STATISTICA, we obtain the
following results.
Std.Err.
of b
Std.Err.
of b*
t(61)
p-value
b*
N=63
Intercept
Speed
-20.2734
3.1366
-6.26038
20.67978
0.000000
0.000000
3.238368
0.935504
0.045238
0.151674
Sums of
df
Mean
p-value
Squares
Squares
59540.15
Effect
59540.15
427.6534
0.000000
Regress.
Residual
1
8492.74
61
139.23
Total
68032.89
Speed X StopDist Y Speed squared StopDist squared Speed StopDist
65853
Total
1195
2471
28719
164951
One of the observations is (X = 39, Y = 138).
The value of the internal studentized residual is
. (final answer to 2 decimal places e.g.
2.12)
Hence, the point (39, 138)
an outlier.
(choose from is or is not)
e 23. You are given : Variance of X= 9. The Regression Equations are:
8X - 10Y+ 66 =0
40X 18 Y= 214
Find:
(1) Average values of X and Y
(i1) Correlation Coefficient between the two variables
(iii) Standard Deviation of Y.
ore
Chapter 4 Solutions
Probability and Statistical Inference (9th Edition)
Ch. 4.1 - For each of the following functions, determine the...Ch. 4.1 - Roll a pair of four-sided dice, one red and one...Ch. 4.1 - Let the joint pmf of X and Y be defined by...Ch. 4.1 - Select an (even) integer randomly from the set...Ch. 4.1 - Each part of Figure 4.1-5 depicts the sample space...Ch. 4.1 - The torque required to remove bolts in a steel...Ch. 4.1 - A particle starts at (0,0) and moves in one-unit...Ch. 4.1 - In a smoking survey among boys between the ages of...Ch. 4.1 - A manufactured item is classified as good, a...Ch. 4.2 - Prob. 1E
Ch. 4.2 - Prob. 2ECh. 4.2 - Roll a fair four-sided die twice. Let X equal the...Ch. 4.2 - Let X and Y have a trinomial distribution with...Ch. 4.2 - Prob. 5ECh. 4.2 - The joint pmf of X and Y is f(x,y)=16,0x+y2, where...Ch. 4.2 - Let the joint pmf of X and Y be...Ch. 4.2 - A certain raw material is classified as to...Ch. 4.2 - Prob. 9ECh. 4.2 - If the correlation coefficient exists, show that...Ch. 4.3 - Let X and Y have the joint pmf...Ch. 4.3 - Let the joint pmf f(x,y) of X and Y be given by...Ch. 4.3 - Let W equal the weight of laundry soap in a...Ch. 4.3 - The gene for eye color in a certain male fruit fly...Ch. 4.3 - Let X and Y have a trinomial distribution with...Ch. 4.3 - An insurance company sells both homeowners...Ch. 4.3 - Using the joint pmf from Exercise 4.2-3, find the...Ch. 4.3 - A fair six-sided die is rolled 30 independent...Ch. 4.3 - Let X and Y have a uniform distribution on the set...Ch. 4.3 - Let fX(x)=110,x=0,1,2,...,9, and...Ch. 4.3 - Suppose that X has a geometric distribution with...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Show that the expression in the exponent of...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Let X and Y have a bivariate normal...Ch. 4.5 - Let X denote the height in centimeters and Y the...Ch. 4.5 - For a freshman taking introductory statistics and...Ch. 4.5 - For a pair of gallinules, let X equal the weight...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Let X and Y have a bivariate normal distribution....Ch. 4.5 - In a college health fitness program, let X denote...Ch. 4.5 - For a female freshman in a health fitness program,...Ch. 4.5 - Prob. 12ECh. 4.5 - An obstetrician does ultrasound examinations on...
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- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardTable 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardUse the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.arrow_forward
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardThe population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?arrow_forwardSuppose an animal scientist, Dr. Dew believes that birth weight (in kg) explains the variation in the length of gestation (in days until birth) for various mammals. To support this fact, he collected data and found out that when the birth weight was x = length of gestation was y = Hint: E,(x; – 7)² = 540, 916.8, E, (y: – 9)² = 195, 233, and E:(yi – ŷ)² = 181, 018. {60, 110, 44, 900, 107} the 241.61+0.162x. {122, 241, 61, 365, 617}. The fitted model was ŷ a) Ignore the birth weight (x). If the length of gestation are independently and identically distributed (i.i.d.) with mean u and variance o?, what is the estimate for u and o?, respectively? b) If you now use the birth weight (x) and assume that the length of gestation are (i.i.d.) with variance o? and mean µ Bo + B1X. (i) Compute the estimate for o?. (ii) By comparison to your estimate in part (a), what does this tell you about this model? c) Construct a 95% confidence interval for the slope parameter.arrow_forward
- A B The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are partially presented in the table with the following results: SST=1564.2, SSR=1227, E(X₁-X)² = 979.7 and Ŷ = 17.7+ 1.12X. D Broker Clients (X) Sales (Y) 1 2 : 12 27 11 : 22 The 95% confidence interval estimate for the slope is 0.471 to 1.932 0.856 to 1.636 0.532 to 1.708 : 0.707 to 1.533 52 37 38 ...... to.....arrow_forward2(a). The following table gives the age distribution of a group of 50 individuals. Age (in years) No. of persons Calculate range and the coefficient of range. (b). If the variables x and y are related by 3x – 2y + 5 = 0 and the range of x is 8, find the range of y 16 - 20 21 – 25 26 - 30 31 36 : 10 15 17 8arrow_forward2arrow_forward
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