Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134506593
Author: James T. McClave, P. George Benson, Terry Sincich
Publisher: PEARSON
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Chapter 1, Problem 1.26ACI
Drafting NFL quarterbacks. The National Football League (NFL) is a lucrative business, generating an annual revenue of about $8 million. One key to becoming a financially successful NFL team is drafting a good quarterback (QB) out of college. The NFL draft allows the worst-performing teams in the previous year the opportunity of selecting the best quarterbacks coming out of college. The Journal of Productivity Analysis (Vol. 35, 2011) published a study of how successful NFL teams are in drafting productive quarterbacks. Data were collected for all 331 quarterbacks drafted between 1970 and 2007. Several variables were measured for each QB, including draft position (one of the top 10 players picked, selection between picks 11 and 50, or selected after pick 50), NFL winning ratio (percentage of games won), and QB production score (higher scores indicate more productive QBs). The researchers discovered that draft position is only weakly related to a quarterback’s performance in the NFL. They concluded that “quarterbacks taken higher [in the draft] do not appear to perform any better.”
- a. What is the experimental unit for this study?
- b. Identify the type (quantitative or qualitative) of each variable measured.
- c. Suppose you want to use this study to project the performance of future NFL QBs. Is this an application of descriptive or
inferential statistics ? Explain.
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We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…
Negate the following compound statement using De Morgans's laws.
Chapter 1 Solutions
Statistics for Business and Economics (13th Edition)
Ch. 1 - What is statistics?Ch. 1 - Explain the difference between descriptive and...Ch. 1 - List and define the four elements of a descriptive...Ch. 1 - List and define the five elements of an...Ch. 1 - List the three major methods of collecting data...Ch. 1 - Explain the difference between quantitative and...Ch. 1 - Explain how populations and variables differ.Ch. 1 - Explain how populations and samples differ.Ch. 1 - What is a representative sample? What is its...Ch. 1 - Why would a statistician consider an inference...
Ch. 1 - Explain the difference between a population and a...Ch. 1 - Define statistical thinking.Ch. 1 - Suppose youre given a data set that classifies...Ch. 1 - Suppose that a population contains 200,000...Ch. 1 - The Random Numbers applet generates a list of n...Ch. 1 - The Random Numbers applet can be used to select a...Ch. 1 - Applying the ConceptsBasic 1.15 Performance-based...Ch. 1 - Jamming attacks on wireless networks. Terrorists...Ch. 1 - Disaggregation of annually reported accounting...Ch. 1 - College application data. Colleges and...Ch. 1 - Opinion polls. Pollsters regularly conduct opinion...Ch. 1 - Cybersecurity survey. The information systems...Ch. 1 - Treasury deficit prior to the Civil War. In Civil...Ch. 1 - The lucky store effect in lottery ticket sales. In...Ch. 1 - Consumer recycling behavior. Under what conditions...Ch. 1 - Who is better at multi-tasking? In business,...Ch. 1 - Zillow.com estimates of home values. Zillow.com is...Ch. 1 - Drafting NFL quarterbacks. The National Football...Ch. 1 - The economic return to earning an MBA. What are...Ch. 1 - Corporate sustainability and firm characteristics....Ch. 1 - Inspection of highway bridges. All highway bridges...Ch. 1 - Structurally deficient highway bridges. Refer to...Ch. 1 - Monitoring product quality. The Wallace Company of...Ch. 1 - Guilt in decision making. The effect of guilt...Ch. 1 - Accounting and Machiavellianism. Behavioral...Ch. 1 - Can money spent on gifts buy love? Is the gift you...Ch. 1 - Random-digit dialing. To ascertain the...Ch. 1 - Current population survey. The employment status...Ch. 1 - Monitoring the production of soft-drink cans. The...Ch. 1 - Sampling TV markets for a court case. A recent...Ch. 1 - Critical Thinking Challenge 1.40 20/20 survey...
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- Negate the following compound statement using De Morgans's laws.arrow_forwardQuestion 6: Negate the following compound statements, using De Morgan's laws. A) If Alberta was under water entirely then there should be no fossil of mammals.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
- Characterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forwardLet G be a connected graph that does not have P4 or C3 as an induced subgraph (i.e.,G is P4, C3 free). Prove that G is a complete bipartite grapharrow_forwardProve sufficiency of the condition for a graph to be bipartite that is, prove that if G hasno odd cycles then G is bipartite as follows:Assume that the statement is false and that G is an edge minimal counterexample. That is, Gsatisfies the conditions and is not bipartite but G − e is bipartite for any edge e. (Note thatthis is essentially induction, just using different terminology.) What does minimality say aboutconnectivity of G? Can G − e be disconnected? Explain why if there is an edge between twovertices in the same part of a bipartition of G − e then there is an odd cyclearrow_forward
- Let G be a connected graph that does not have P4 or C4 as an induced subgraph (i.e.,G is P4, C4 free). Prove that G has a vertex adjacent to all othersarrow_forwardWe consider a one-period market with the following properties: the current stock priceis S0 = 4. At time T = 1 year, the stock has either moved up to S1 = 8 (with probability0.7) or down towards S1 = 2 (with probability 0.3). We consider a call option on thisstock with maturity T = 1 and strike price K = 5. The interest rate on the money marketis 25% yearly.(a) Find the replicating portfolio (φ, ψ) corresponding to this call option.(b) Find the risk-neutral (no-arbitrage) price of this call option.(c) We now consider a put option with maturity T = 1 and strike price K = 3 onthe same market. Find the risk-neutral price of this put option. Reminder: A putoption gives you the right to sell the stock for the strike price K.1(d) An investor with initial capital X0 = 0 wants to invest on this market. He buysα shares of the stock (or sells them if α is negative) and buys β call options (orsells them is β is negative). He invests the cash balance on the money market (orborrows if the amount is…arrow_forwardDetermine if the two statements are equivalent using a truth tablearrow_forward
- Question 4: Determine if pair of statements A and B are equivalent or not, using truth table. A. (~qp)^~q в. р л~9arrow_forwardDetermine if the two statements are equalivalent using a truth tablearrow_forwardQuestion 3: p and q represent the following simple statements. p: Calgary is the capital of Alberta. A) Determine the value of each simple statement p and q. B) Then, without truth table, determine the va q: Alberta is a province of Canada. for each following compound statement below. pvq р^~q ~рл~q ~q→ p ~P~q Pq b~ (d~ ← b~) d~ (b~ v d) 0 4arrow_forward
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