Introduction to Business Statistics
7th Edition
ISBN: 9781111792374
Author: WEIERS
Publisher: Cengage Learning
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Textbook Question
Chapter 5.5, Problem 5.30E
What is the difference between a marginal probabilitiy and a joint
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The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c.
Question content area bottom
Part 1
a. Develop a simple linear regression model between billable hours and overhead costs.
Overhead
Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable
Hours
(Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.)
Part 2
b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm?
Interpret the fixed term,
b 0b0,
if appropriate. Choose the correct answer below.
A.
The value of
b 0b0
is the predicted billable hours for an overhead cost of 0 dollars.
B.
It is not appropriate to interpret
b 0b0,
because its value…
Using the accompanying Home Market Value data and associated regression line,
Market ValueMarket Valueequals=$28,416+$37.066×Square
Feet, compute the errors associated with each observation using the formula
e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi
and construct a frequency distribution and histogram.
LOADING...
Click the icon to view the Home Market Value data.
Question content area bottom
Part 1
Construct a frequency distribution of the errors,
e Subscript iei.
(Type whole numbers.)
Error
Frequency
minus−15 comma 00015,000less than<
e Subscript iei
less than or equals≤minus−10 comma 00010,000
0
minus−10 comma 00010,000less than<
e Subscript iei
less than or equals≤minus−50005000
5
minus−50005000less than<
e Subscript iei
less than or equals≤0
21
0less than<
e Subscript iei
less than or equals≤50005000
9…
The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c
Overhead Costs Billable Hours345000 3000385000 4000410000 5000462000 6000530000 7000545000 8000
Chapter 5 Solutions
Introduction to Business Statistics
Ch. 5.2 - The president of a computer manufacturing firm...Ch. 5.2 - Prob. 5.2ECh. 5.2 - Prob. 5.3ECh. 5.2 - Prob. 5.4ECh. 5.2 - Regarding Exercise 5.4, how might an observer...Ch. 5.2 - Prob. 5.6ECh. 5.2 - Prob. 5.7ECh. 5.2 - Prob. 5.8ECh. 5.2 - If the odds are 4:7 that an event will occur, what...Ch. 5.3 - A sample space includes the events A. B. and C....
Ch. 5.3 - A sample space includes the events A, B, and C....Ch. 5.3 - The following contingency table of frequencies is...Ch. 5.3 - Using the table in Exercise 5.12, how many victims...Ch. 5.3 - Using the table in Exercise 5.12, what is the...Ch. 5.3 - Prob. 5.15ECh. 5.3 - Using the table in Exercise 5.15, assume that one...Ch. 5.3 - The owner of a McDonald’s restaurant in France is...Ch. 5.3 - Prob. 5.18ECh. 5.3 - According to data from the U.S. Energy Information...Ch. 5.3 - There are 100 males and 120 females in the...Ch. 5.4 - A financial advisor frequently holds investment...Ch. 5.4 - A survey of employees at a large company found the...Ch. 5.4 - In 2008, McDonald’s had 31,967 restaurants...Ch. 5.4 - For three mutually exclusive events...Ch. 5.4 - It has been reported that the 49,600 employees of...Ch. 5.4 - In 2003, Intergy Corporation had 2,631,752...Ch. 5.4 - According to the Bureau of Labor Statistics, there...Ch. 5.4 - Using the information presented in the table in...Ch. 5.4 - Using the infomation presented in the table in...Ch. 5.5 - What is the difference between a marginal...Ch. 5.5 - Prob. 5.31ECh. 5.5 - Prob. 5.32ECh. 5.5 - It has been reported that 57% of U.S. households...Ch. 5.5 - A fair coin is tossed three times. What is the...Ch. 5.5 - A kitchen appliance has 16 working parts, each of...Ch. 5.5 - An optometry practitioner group has found that...Ch. 5.5 - Through April 30 of the 2009 filing season, 15.8%...Ch. 5.5 - Of employed U.S. adults age 25 or older, 90.4%...Ch. 5.5 - A taxi company in a small town has two cabs. Cab A...Ch. 5.5 - Using the table in Exercise 5.12, calculate the...Ch. 5.5 - Charlie has read a survey result that says 60% of...Ch. 5.5 - Prob. 5.42ECh. 5.5 - Based on the information in Exercise 5.21, if the...Ch. 5.5 - Based on the information in Exercise 5.22, if a...Ch. 5.6 - For U.S. live births, P(boy) and P(girl) are...Ch. 5.6 - Using the information in Exercise 5.45, assume...Ch. 5.6 - A magician has two coins: One is unbalanced and...Ch. 5.6 - For the information provided in Exercise 5.39, the...Ch. 5.6 - Machine A produce 3% defectives, machine B produce...Ch. 5.7 - A tax accountant has three choices for the method...Ch. 5.7 - A committee consists of eight members, each of...Ch. 5.7 - Ten prominent citizens have been nominated for a...Ch. 5.7 - Prob. 5.53ECh. 5.7 - A state’s license plate has 6 positions, each of...Ch. 5.7 - When we are considering n objects taken r at a...Ch. 5.7 - An investment counselor would like to meet with 12...Ch. 5.7 - Flow many different combinations are possible if 6...Ch. 5.7 - A roadside museum has 25 exhibits but enough space...Ch. 5.7 - A sales representative has 35 customers throughout...Ch. 5 - It has been estimated that the odds of being...Ch. 5 - A fast-food chain gives each customer a coupon,...Ch. 5 - For the situation in Exercise 5.61, what is the...Ch. 5 - The “daily number” of a state lottery is a 3-digit...Ch. 5 - The U.S. Bureau of Justice released the following...Ch. 5 - For the three perpetrators in Exercise 5.64,...Ch. 5 - Dave has been arrested for arson and has been...Ch. 5 - A firm has two computer systems available for...Ch. 5 - An industrial hoist is being used in an emergency...Ch. 5 - The following relative frequency distribution...Ch. 5 - Collecting data on traffic accident fatalities,...Ch. 5 - During fiscal 1995, Ashland Exploration drilled 7...Ch. 5 - Avis, Inc., has reported that its fleet consists...Ch. 5 - Data from the Federal Bureau of Investigation show...Ch. 5 - Of the participants in a corporate meeting. 20%...Ch. 5 - Of the adults in Jefferson Count, 10% have had CPR...Ch. 5 - Over the years, a realtor estimates that 50% of...Ch. 5 - Prob. 5.77CECh. 5 - Prob. 5.78CECh. 5 - When a machine is properly calibrated, 0.5% of its...Ch. 5 - In examining borrower characteristics versus loan...Ch. 5 - Prob. 5.81CECh. 5 - A corporate board of directors consisting of 15...Ch. 5 - Prob. 5.83CECh. 5 - A test to compare the taste of 6 soft drinks is...Ch. 5 - A certain brand of bicycle lock requires that each...
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- Using the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416plus+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. Square Feet Market Value1813 911001916 1043001842 934001814 909001836 1020002030 1085001731 877001852 960001793 893001665 884001852 1009001619 967001690 876002370 1139002373 1131001666 875002122 1161001619 946001729 863001667 871001522 833001484 798001589 814001600 871001484 825001483 787001522 877001703 942001485 820001468 881001519 882001518 885001483 765001522 844001668 909001587 810001782 912001483 812001519 1007001522 872001684 966001581 86200arrow_forwarda. Find the value of A.b. Find pX(x) and py(y).c. Find pX|y(x|y) and py|X(y|x)d. Are x and y independent? Why or why not?arrow_forwardThe PDF of an amplitude X of a Gaussian signal x(t) is given by:arrow_forward
- The PDF of a random variable X is given by the equation in the picture.arrow_forwardFor a binary asymmetric channel with Py|X(0|1) = 0.1 and Py|X(1|0) = 0.2; PX(0) = 0.4 isthe probability of a bit of “0” being transmitted. X is the transmitted digit, and Y is the received digit.a. Find the values of Py(0) and Py(1).b. What is the probability that only 0s will be received for a sequence of 10 digits transmitted?c. What is the probability that 8 1s and 2 0s will be received for the same sequence of 10 digits?d. What is the probability that at least 5 0s will be received for the same sequence of 10 digits?arrow_forwardV2 360 Step down + I₁ = I2 10KVA 120V 10KVA 1₂ = 360-120 or 2nd Ratio's V₂ m 120 Ratio= 360 √2 H I2 I, + I2 120arrow_forward
- Q2. [20 points] An amplitude X of a Gaussian signal x(t) has a mean value of 2 and an RMS value of √(10), i.e. square root of 10. Determine the PDF of x(t).arrow_forwardIn a network with 12 links, one of the links has failed. The failed link is randomlylocated. An electrical engineer tests the links one by one until the failed link is found.a. What is the probability that the engineer will find the failed link in the first test?b. What is the probability that the engineer will find the failed link in five tests?Note: You should assume that for Part b, the five tests are done consecutively.arrow_forwardProblem 3. Pricing a multi-stock option the Margrabe formula The purpose of this problem is to price a swap option in a 2-stock model, similarly as what we did in the example in the lectures. We consider a two-dimensional Brownian motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices are modeled by the following equations: dX = dY₁ = X₁ (rdt+ rdt+0₁dW!) (²)), Y₁ (rdt+dW+0zdW!"), with Xo xo and Yo =yo. This corresponds to the multi-stock model studied in class, but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure P is already the risk-neutral measure (Both stocks have rate of return r). We write σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to exchange one share of X for one share of Y. That is, the option has payoff F=(Yr-XT). (a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for the process Xt. Reminder before proceeding to question (b): Girsanov's theorem…arrow_forward
- Problem 1. Multi-stock model We consider a 2-stock model similar to the one studied in class. Namely, we consider = S(1) S(2) = S(¹) exp (σ1B(1) + (M1 - 0/1 ) S(²) exp (02B(2) + (H₂- M2 where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with t≥0 Cov (B(¹), B(2)) = p min{t, s}. " The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian motion (W+)+20 (W(1), W(2))+20 such that = S(1) S(2) = = S(¹) exp (011W(¹) + (μ₁ - 01/1) t) 롱) S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t). where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p). Hint: The constants will follow the formulas developed in the lectures. (a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2) functions of (B(1), B(²)). as (b) Using the formulas obtained in (a), show that the process (WA) is actually a 2- dimensional standard Brownian motion (i.e. show that each component is normal, with mean 0, variance t, and that their…arrow_forwardThe scores of 8 students on the midterm exam and final exam were as follows. Student Midterm Final Anderson 98 89 Bailey 88 74 Cruz 87 97 DeSana 85 79 Erickson 85 94 Francis 83 71 Gray 74 98 Harris 70 91 Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary. Test statistic: rs =arrow_forwardBusiness discussarrow_forward
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