Student Solutions Manual for Basic Business Statistics
13th Edition
ISBN: 9780321926708
Author: David M. Levine; Mark L. Berenson; Timothy C. Krehbiel; Kathryn A. Szabat; David F. Stephan
Publisher: Pearson Education
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Chapter 13, Problem 43PS
a.
To determine
Determine if there is evidence of a linear relationship between the summated ratings of a restaurant and the cost of a meal.
b.
To determine
Calculate a
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Students have asked these similar questions
One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey.
Preference
Male
Female
TOTAL
Prefers dogs
\[36\]
\[20\]
\[56\]
Prefers cats
\[10\]
\[26\]
\[36\]
No preference
\[2\]
\[6\]
\[8\]
TOTAL
\[48\]
\[52\]
\[100\]
problem 1
Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal.
\[P\left(\text{prefers dogs}\right)=\]
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Hide explanation
Preference
Male
Female
TOTAL
Prefers dogs
\[\blueD{36}\]
\[\blueD{20}\]
\[\blueE{56}\]
Prefers cats
\[10\]
\[26\]
\[36\]
No preference
\[2\]
\[6\]
\[8\]
TOTAL
\[48\]
\[52\]
\[100\]
There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.
Business discuss
You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below.
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship.
Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size).
Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear regression model.
Interpret the…
Chapter 13 Solutions
Student Solutions Manual for Basic Business Statistics
Ch. 13 - Prob. 1PSCh. 13 - If the values of X in Problem 13.1 from 2 to 25,...Ch. 13 - Fitting a straight line to a set data yields the...Ch. 13 - The production of wine is a multibillion-dollar...Ch. 13 - Zagat’s publishes restaurant ratings for various...Ch. 13 - The owner of a moving company typically has his...Ch. 13 - Starbucks Coffee Co. uses a data-based approach to...Ch. 13 - Prob. 8PSCh. 13 - An agent for a residential real estate company in...Ch. 13 - Prob. 10PS
Ch. 13 - How do you interpret a coefficient by of...Ch. 13 - If SSR= 36 and SSE=4, determine SST and then...Ch. 13 - If SSR=66 and SST=88, Compute the coefficient of...Ch. 13 - If SSE= 10 and SSR=30, compute the coefficient of...Ch. 13 - If SSR=120, Why is it impossible for SST to equal...Ch. 13 - In problem 13.4 on page 493, the percentage of...Ch. 13 - Prob. 17PSCh. 13 - Prob. 18PSCh. 13 - In Problem 13.7 on page 494, you used the plate...Ch. 13 - In problem 13.8 on page 494, you used annual...Ch. 13 - In problem 13.9 on page 494, an agent for a real...Ch. 13 - In Problem 13.10 on page 501, you used box office...Ch. 13 - The following results provide the X Values,...Ch. 13 - The following results show the X Values,...Ch. 13 - In problem 13.5 on page 493, you used the summated...Ch. 13 - In problem 13.4 on page 493, you used the...Ch. 13 - In problem 13.7 on page 494, you used the plate...Ch. 13 - In Problem 13.6 on page 501, the owner of a moving...Ch. 13 - In problem 13.9 on page 494, an agent for a real...Ch. 13 - Prob. 30PSCh. 13 - In problem 13.10 on page 501, you used box office...Ch. 13 - The residuals for 10 consecutive time periods are...Ch. 13 - The residuals for 15 consecutive time periods are...Ch. 13 - In Problem 13.7 on page 494 concerning the...Ch. 13 - What is the relationship between the price of...Ch. 13 - Prob. 36PSCh. 13 - A freshly brewed shot of espresso has three...Ch. 13 - The owners of a chain of ice cream stores have the...Ch. 13 - You are testing the null hypothesis that there is...Ch. 13 - Prob. 40PSCh. 13 - Prob. 41PSCh. 13 - In problem 13.4 on page 493, you used the...Ch. 13 - Prob. 43PSCh. 13 - Prob. 44PSCh. 13 - In Problem 13.7 on page 494, you used the plate...Ch. 13 - Prob. 46PSCh. 13 - In Problem 13.9 on page 494, an agent for a real...Ch. 13 - In Problem 13.10 on page 501, you used box office...Ch. 13 - Prob. 49PSCh. 13 - Prob. 50PSCh. 13 - Prob. 51PSCh. 13 - Movie companies need to predict the gross receipts...Ch. 13 - Prob. 53PSCh. 13 - A survey by the Pew Research Center found that...Ch. 13 - Prob. 55PSCh. 13 - Based on a sample of n=20, the latest-squares...Ch. 13 - In Problem 133 on page 500, you used the summated...Ch. 13 - In Problem 13.4 on page 493, you used the...Ch. 13 - In Problem 13.7 on page 494, you used the plate...Ch. 13 - Prob. 60PSCh. 13 - Prob. 61PSCh. 13 - Prob. 62PSCh. 13 - Prob. 63PSCh. 13 - Prob. 64PSCh. 13 - Prob. 65PSCh. 13 - When is the unexplained variation (i.e., error sum...Ch. 13 - Prob. 67PSCh. 13 - Prob. 68PSCh. 13 - Prob. 69PSCh. 13 - How do you evaluate the assumptions of regression...Ch. 13 - When and how do you use the Durbin-Watson...Ch. 13 - Prob. 72PSCh. 13 - Can you use Twitter activity to forecast box...Ch. 13 - Management of a soft-drink bottling company has...Ch. 13 - Measuring the height of a California redwood tree...Ch. 13 - You want to develop a model to predict the...Ch. 13 - Prob. 77PSCh. 13 - The director of graduate studies at a large...Ch. 13 - An accountant for a large department store has the...Ch. 13 - On January 28, 1986, the space shuttle Challenger...Ch. 13 - A baseball analyst would like to study various...Ch. 13 - Can you use the annual revenues generated by...Ch. 13 - In Problem 13.82 you used annual revenue to...Ch. 13 - During the fall harvest season in the United...Ch. 13 - Prob. 85PSCh. 13 - The file CEO 2016 includes the total compensation...Ch. 13 - In Problem 13.8, 13.20, 13.30, 13.46, 13.62,...
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- Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. How to take snapshots: if you use a MacBook, press Command+ Shift+4 to take snapshots. If you are using Windows, use the Snipping Tool to take snapshots. Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship. Value of correlation coefficient: Direction of the relationship (positive, negative, or zero relationship): Strength of the relationship (strong/moderate/weak): Question 2: Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardProblem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forward
- We consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forwardQuestion 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward
- 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…arrow_forwardUsing 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…arrow_forwardThe 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 8000arrow_forward
- 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
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